Dissertations / Theses on the topic 'Black holes (Astronomy) – Mathematics'

Over recent years there has been an increase of the number of secure supermassive black hole (SMBH) detections. These SMBH measurements have lead astronomers to establish well defined empirical relationships between the SMBH mass and some of the properties of the host galaxy. The number of galaxies with SMBH mass measurements is currently limited to about 100. One approach of expanding the study of the SMBH is to use the empirical relations for estimating M[subscript(bh)] for larger samples of galaxies. The investigation of the SMBH population (or SMBH mass function) for large sample of galaxies in the nearby universe has helped to constrain the SMBH and the galaxy evolution. Previous estimates of the SMBH mass function at low redshift were produced mainly by combining the measurements of the galaxy luminosity or velocity function with one of the SMBH scaling relations. In the first part of the thesis I will present an independent construction of the nearby supermassive black hole mass function by applying the optical M[subscript(bh)]–L relation onto the Millennium Galaxy Catalogue (MGC). Additionally, in the second part I will provide photometric analysis of all UKIDSS galaxies for which SMBH masses have been measured. I will derive composite profiles of brightness, ellipticity and position angles of each galaxy. I will show that the Sérsic function fits the brightness profile of the majority of the elliptical galaxies and the bulge of disk galaxies and I will provide alternative multi-component fits when necessary. Then these photometric parameters will be used for constructing the M[subscript(bh)]–L relation in the near-IR and to investigate the M[subscript(bh)]–n relation. In the third part I will construct the near-IR SMBH mass function for the Galaxy and Mass Assembly (GAMA) survey. For this purpose I will apply the newly derived M[subscript(bh)]–L relation onto an elliptical subsample of K-band images. The advantage of this SMBH mass function is that during the M[subscript(bh)]–L construction I used the same quality images and techniques used on the GAMA survey. Apart from the M[subscript(bh)]–L relation, the M[subscript(bh)]–sigma relation was used as an alternative approach for a subsample of galaxies for which the velocity dispersions were available. Furthermore, I employed both local SMBH mass functions (MGC & GAMA) for estimating the SMBH mass density at redshift zero and accounted for the dependence of the total SMBH density on the look-back time by comparing with semi-analytic SMBH mass functions. Finally, from the SMBH mass density I estimated the baryon fraction that is locked into SMBHs.

The fuzzball model of a black hole is an attempt to resolve the many paradoxes and puzzles of black hole physics that have revealed themselves over the last century. These badly behaved solutions of general relativity have given physicists one of the few laboratories to test candidate quantum theories of gravity. Though little is known about exactly what lies beyond the event horizon, and what the ultimate fate of matter that falls in to a black hole is, we know a few intriguing and elegant semi-classical results that have kept physicists occupied. Among these are the known black hole entropy and the Hawking radiation process.

Hawking radiation, despite its presence in theoretical physics for over thirty years, remains elusive and undetected. It also suffers, in its original context of gravitational black holes, from conceptual difficulties. Of particular note is the trans-Planckian problem, which is concerned with the apparent origin of the radiation in absurdly high frequencies. In order to gain better theoretical understanding and, it is hoped, experimental verification of Hawking radiation, much study is being devoted to systems which model the spacetime geometry of black holes, and which, by analogy, are also thought to emit Hawking radiation. These analogue systems typically exhibit dispersion, which regularizes the wave behaviour at the horizon but does not lend itself well to analytic treatment, thus rendering Hawking’s prediction less secure. A general analytic method for dealing with Hawking radiation in dispersive systems has proved difficult to find. This thesis presents new numerical and analytic results for Hawking emission spectra in dispersive systems. It examines two black-hole analogue systems: it begins by introducing the well-known acoustic model, presenting some original results in that context; then, through analogy with the acoustic model, goes on to develop the lesser-known fibre-optical model. The following original results are presented in the context of both of these models: • an analytic expression for the low-frequency temperature is found for a hyperbolic tangent background profile, valid in the entire parameter space; it is well-known that the spectrum is approximately thermal at low frequencies, but a universally valid expression for the corresponding temperature is an original development; • an analytic expression for the spectrum, valid over almost the entire frequency range, when the velocity profile parameters lie in the regime where the low-frequency temperature is given by the Hawking prediction; previous work has focused on the low-frequency thermal spectrum and the characterization of the deviations from thermality, rather than a single analytic expression; and • a new unexplored regime where no group-velocity horizon exists is examined; the Hawking spectra are found to be non-zero here, but also highly non-thermal, and are found, in the limit of small deviations, to vary with the square of the maximum deviation; the analytic expression for the case with a horizon is found to carry over to this new regime, with appropriate modifications. Furthermore, the thesis examines the results of a classical frequency-shifting experiment in the context of fibre-optical horizons. The theory of this process is presented for both a constant-velocity and a constantly-decelerating pulse, the latter case taking account of the Raman effect. The resulting spectra are at least qualititively explained, but there is a discrepancy between theory and experiment that has not yet been accounted for.

In this thesis, we study toy models of two-dimensional gravity. We first review two known models: the classical and quantum corrected CGHS models and the quantum corrected model of RST. These two models have black holes solutions with curvature singularities, similar to the Schwartzschild black hole. This singularity becomes naked in the RST model at a certain event during the evaporation. In the third chapter, we build a more general version with new quantum corrections beyond those presented in the RST model, which enable us to find a model without curvature singularities. We will also see that these new quantum corrections can affect the rate of Hawking radiation flowing from the black hole.

In this thesis we investigate selection effects in astrophysical observations. We demonstrate that the determination of the quasar black hole mass function and Eddington ratio distribution via observations are biased. By modelling the quasar selection function and the black hole mass measurement process we show that one is able to infer the true distribution of physical quantities from observations. We present the intrinsic accretion rates of AGN, the intrinsic accretion rates and the black hole mass function for optically selected quasars up to redshift of two. The results show that the Eddington limit continues to be a real physical limit to black hole accretion. We present a new upper limit of black hole masses from the inferred intrinsic black hole mass function and demonstrate the need of a mass dependent accretion rate in accordance with down sizing. Finally we investigate correlations between radio luminosity and observed black hole mass for optically selected quasars. We first show that mixing of fiat and steep spectrum quasars leads to results that are dependent on the observing frequency, and therefore should be treated with caution. We demonstrate that beaming of the radio core together with an orientation dependent optical selection effect can give rise to a bimodal distribution in the radio luminosities of optically selected quasars.

Active Galactic Nuclei (AGNs) are believed to be powered by accretion onto supermassive black holes (BHs). With the development in high resolution observations over a broad frequency range, it is now tenable to study the corresponding physical processes in detail. We find that the emission from the closest supermassive BH candidate, Sagittarius A*, a compact radio source presumably accreting from stellar winds prevailing at the Galactic Center, can be explained as due to a quasi-spherical accretion flow, which circularizes to form a small magnetized accretion disk near the BH's event horizon. The mm/sub-mm and X-ray emissions are produced via thermal synchrotron processes and their self-Comptonization, respectively, in the inner ten Schwarzschild radii of the resultant Keplerian structure. The cm radio emission, however, appears to be produced by non-thermal synchrotron processes in the circularization zone. The recently detected X-ray flare seems to indicate a transient enhancement of mass accretion rate through the inner accretion disk. The 106-day cycle seen at 2.0 cm and 1.3 cm, on the other hand, suggests that the disk is precessing around a spinning BH, whose spin may be determined by timing observation of Sgr A* at mm/sub-mm wavelengths. Our tentative observational result is consistent with this magnetized disk model. The supermassive BH M31*, a compact radio source in the nucleus of M31, has many features in common with Sgr A*, yet their differences are significant. We show that the accretion model being developed for Sgr A* comprises two branches of solutions, distinguished by the relative importance of cooling compared to compressional heating at the capture radius. Sgr A* is presumably a 'hot' BH. While M31* seems to be a member of the 'cold' BH family. The study of the nuclei in radio galaxies reveals many new characteristics of the large scale accretion flows. In NGC 4261, we show that a turbulence-dominated disk, illuminated by its AGN, can not only account for the observed sub-parsec scale radio gap in the core, but also produce the optical broad lines emitted from the region. However, the prominent radio jets distinguish such BHs from those in the compact radio sources. The relativistic jets are probably driven by the action of supermassive, fast spinning BHs. Our study on NGC 6251* indicates that the initial ejection of matter can be associated with the thermal expansion of the accreted gas, which is heated by a spinning BH near its even horizon.

Measuring black hole spin has become a key topic in astrophysics, and recent focus on the spin powering of jets in X-ray binaries has heightened the need for accurate measurements of spin. However, the effects of spin are subtle, and are only imprinted on emission from very close to the black hole. This is revealed since the black hole spin defines the radius of the last stable orbit of the accretion disc, which is smaller for larger spin. Recent advances in X-ray observatories and spectroscopic techniques have enabled spin estimates for a number of black holes in X-ray binaries,but the accuracy of these methods, and the link between spin and jet power,have become very controversial subjects. In this thesis I address the former of these problems through X-ray reflection, which is one of two leading X-ray spectroscopic methods to measure black hole spin (the other being the ‘continuum’ method). Firstly, I investigate the systematic uncertainties associated with the X-ray reflection technique, and display how model degeneracies can severely affect the determination of spin. After establishing these potential flaws I then performed a systematic study of X-ray reflection during four hard state observations of the black hole GX 339−4, and show that the relativistic effects vary significantly over two orders of magnitude in luminosity. I show that this requires the accretion disc to be substantially truncated from the last stable orbit that is used to measure spin, thus rendering spin estimates impossible in the hard state. Following this I analyse over 500 archival observations of the same source with the Rossi Timing X-ray Explorer. Whilst these data cannot directly measure the inner disc radius, they allow a quantitative investigation of how X-ray reflection and the power-law co-evolve. Since the latter gives rise to the former, this allows changes in the accretion geometry to be revealed, which I show to be consistent with a truncated accretion disc in the hard state, and a gradual collapse of the corona in the soft state. Finally, I present three recent observations of GX 339−4 in the hard state with XMM-Newton, which allow an unprecedented simultaneous constraint on the inner accretion disc radius via the reflection and continuum methods. The two techniques agree, and present further compelling evidence for accretion disc truncation in the hard state.

The thesis begins with a study of the origin of non-linear cosmological fluctuations. In particular, a class of models of multiple field inflation are considered, with specific reference to those cases in which the non-Gaussian correlation functions are large. The analysis shows that perturbations from an almost massless auxiliary field generically produce large values of the non-linear parameter fNL. Next, the effects of including non-Gaussian correlation functions in the statistics of cosmological structure are explored. For this purpose, a non-Gaussian probability distribution function (PDF) for the curvature perturbationR is required. Such a PDF is derived from first principles in the context of quantum field theory, with n-point correlation functions as the only input. Under reasonable power-spectrum conditions, an explicit expression for the PDF is presented, with corrections to the Gaussian distribution from the three-point correlation function hRRRi. The method developed for the derivation of the non-Gaussian PDF is then used to explore two important problems in the physics of primordial black holes (PBHs). First, the non-Gaussian probability is used to compute corrections to the number of PBHs generated from the primordial curvature fluctuations. Particular characteristics of such corrections are explored for a variety of inflationary models. The non-Gaussian corrections explored consist exclusively of non-vanishing three-point correlation functions. The second application concerns new cosmological observables. The formation of PBHs is known to depend on two main physical characteristics: the strength of the gravitational field produced by the initial curvature inhomogeneity and the pressure gradient at the edge of the curvature configuration. The latter has so far been ignored in the estimation of the probability of PBH formation. We account for this by using two parameters to describe the profile: The amplitude of the inhomogeneity and its second radial derivative, both evaluated at the centre of the configuration. The method developed to derive the non-Gaussian PDF is modified to find the joint probability of these two parameters. We discuss the implications of the derived probability for the fraction of mass in the universe in the form of PBHs.

Understanding the formation and evolution of galaxies is one of the primary research goals of astronomy today. Galaxies are observed to have a range of masses, colours and morphologies, and various processes, including feedback, have been proposed to explain these differences. Some of these processes are related to the environment in which a galaxy resides. In this Thesis I present the results of three projects I have undertaken to help increase our understanding of galaxy formation. The first was to investigate the different methods of structure detection used in simulations. Placing an identical subhalo at different radii inside a larger halo demonstrated that subhalo mass recovery is radially dependent. Subhaloes closer to the centre of a halo are recovered smaller than haloes near the edge, but their peak circular velocity is less affected. The second project set about investigating different ways of measuring galaxy environment. Observationally galaxy environment is most commonly measured through nearest neighbours or fixed apertures, and these have different relationships to the underlying dark matter haloes. Fixed aperture measures are sensitive to halo mass and best probe the `large-scale environment' external to a halo. Meanwhile nearest neighbour measures are insensitive to halo mass and best probe the `local environment' internal to a halo. The final project involved implementing the Accretion Disc Particle (ADP) model of black hole growth within a cosmological, large volume simulation, including cooling, star formation and feedback. Comparing this method with a modified Bondi-Hoyle model allows for the investigation of how accretion rates affect feedback and galaxy properties. ADP suffers from the limited resolution of large-scale simulations and produces unphysically large accretion discs. Both models can reproduce the local black hole scaling relations, but produce black hole mass functions that do not agree with observations.

Thesis (Ph. D.)--Ohio State University, 2004.
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An understanding of radiation is paramount for connecting observations of accretion disks with the theory of black holes. In this thesis, we explore via radiative transfer postprocessing calculations the observational signatures of black holes. We investigate disk spectra by analyzing general relativistic magnetohydrodynamic (GRMHD) simulations of accretion disks. For the most part there are no surprises -- the resulting GRMHD spectrum is very close to the analytic Novikov & Thorne (1973) prediction from decades past, except for a small modification in the case of spinning black holes, which exhibit a high-energy power-law tail that is sourced by hot Comptonized gas from within the plunging region of the accretion flow. These conclusions are borne out by both 1D and 3D radiative transfer calculations of the disk. Significant effort was spent in developing from scratch the 3D radiative code that we used for the analysis. The code is named HERO (Hybrid Evaluator for Radiative Objects) and it is a new general purpose grid-based 3D general relativistic radiative solver.
Astronomy

Mergers of a neutron star and a black hole are interesting because of the dual complexity of the black hole's strong gravity and the neutron star's nuclear-density fluid. Mergers can yield short-lived nuclear accretion disks, emitting copious neutrinos. This radiation may change the thermodynamic state of the disk itself, may drive an ultrarelativistic jet of electrons and positrons, may oscillate in its flavor content, may irradiate surrounding matter, playing a role in nucleosynthesis, and may be detected directly.

In this thesis I present a model of such a merger, its remnant accretion disk, and its neutrino emission. In particular, we evolve a neutron star—black hole merger through ∼100 ms, solving the full general relativistic hydrodynamics equations, from inspiral through merger and accretion epochs. We treat the neutrinos approximately, using a leakage framework, which accounts for local energy losses and composition drift in the fluid due to escaping neutrinos. We use geodesic ray tracing on a late time slice of the model to calculate the full spatial-, angular-, and energy-dependence of the neutrino distribution function around the accretion disk. This distribution then serves in a computation of the energy available to form a jet via neutrino-antineutrino annihilation in the disk funnel. In this scenario, we find that enough energy is deposited to drive a jet of short-gamma-ray-burst-energy by neutrino processes alone.

This thesis is divided in two parts: the first part is dedicated to the study of black hole solutions in a theory of modified gravity, called massive gravity, that may be able to explain the actual stage of accelerated expansion of the Universe, while in the second part we focus on constraining primordial black holes as dark matter candidates.

In particular, during the first part we study the thermodynamical properties of specific black hole solutions in massive gravity. We conclude that such black hole solutions do not follow the second and third of law of thermodynamics, which may signal a problem in the model. For instance, a naked singularity may be created as a result of the evolution of a singularity-free state.

In the second part, we constrain primordial black holes as dark matter candidates. To do that, we consider the effect of primordial black holes when they interact with compact objects, such as neutron stars and white dwarfs. The idea is as follows: if a primordial black hole is captured by a compact object, then the accretion of the neutron star or white dwarf’s material into the hole is so fast that the black hole destroys the star in a very short time. Therefore, observations of long-lived compact objects impose constraints on the fraction of primordial black holes. Considering both direct capture and capture through star formation of primordial black holes by compact objects, we are able to rule out primordial black holes as the main component of dark matter under certain assumptions that are discussed.

To better understand the relevance of these subjects in modern cosmology, we begin the thesis by introducing the standard model of cosmology and its problems. We give particular emphasis to modifications of gravity, such as massive gravity, and black holes in our discussion of the dark sector of the Universe./

Cette thèse est divisée en deux parties :la première partie est consacrée à l’étude de certaines solutions de trous noirs dans une théorie modifiée de la gravité, appelée la gravité massive, qui peut être en mesure d’expliquer l’expansion accélérée de l’Univers; tandis que dans la seconde partie, nous nous concentrons sur des contraintes sur les trous noirs primordiaux comme candidats de matière noire.

En particulier, au cours de la première partie, nous étudions les propriétés thermodynamiques de solutions spécifiques de trous noirs en gravité massive. Nous en concluons que ces solutions de trous noirs ne suivent ni la deuxième, ni la troisième loi de la thermodynamique, ce qui semble indiquer une inconsistance dans le modèle. Par exemple, une singularité nue peut être créée à la suite de l’évolution d’un état sans aucune singularité.

Dans la deuxième partie, nous mettons des contraintes sur les trous noirs primordiaux en tant que candidats de matière noire. Pour ce faire, nous considérons l’effet des trous noirs primordiaux lorsqu’ils interagissent avec des objets compacts, tels que les étoiles à neutrons et les naines blanches. L’idée est comme suit :si un trou noir primordial est capturé par un objet compact, alors l’accrétion du matériel constituant l’étoile à neutrons ou la naine blanche est si rapide que le trou noir détruit l’étoile en un temps très court. Par conséquent, les observations d’objets compacts imposent des contraintes sur la fraction de trous noirs primordiaux. Considérant à la fois la capture directe des trous noirs primordiaux par les objets compacts et la capture au travers de la formation stellaire, nous sommes en mesure d’exclure les trous noirs primordiaux comme la composante principale de matière noire sous certaines hypothèses qui sont discutées.

Pour mieux comprendre la pertinence de ces sujets dans la cosmologie moderne, nous commençons la thèse par l’introduction du modèle standard de la cosmologie et de ses problèmes. Nous donnons une importance particulière aux modifications de la gravité, telles que la gravité massive, et aux trous noirs dans notre discussion sur le secteur sombre de l’Univers.
Doctorat en Sciences
info:eu-repo/semantics/nonPublished

This work investigates how black holes can be described in terms of different definitions of horizons. Global definitions in terms of event horizons and Killing horizons are contrasted with local definitions in terms of trapping horizons and dynamical horizons. The discussion is framed in the context of the laws of black hole thermodynamics.

Supermassive black holes are a fundamental component of the universe in general and of galaxies in particular. Almost every massive galaxy harbours a supermassive black hole (SMBH) in its center. Furthermore, there is a close connection between the growth of the SMBH and the evolution of its host galaxy, manifested in the relationship between the mass of the black hole and various properties of the galaxy's spheroid component, like its stellar velocity dispersion, luminosity or mass. Understanding this relationship and the growth of SMBHs is essential for our picture of galaxy formation and evolution. In this thesis, I make several contributions to improve our knowledge on the census of SMBHs and on the coevolution of black holes and galaxies. The first route I follow on this road is to obtain a complete census of the black hole population and its properties. Here, I focus particularly on active black holes, observable as Active Galactic Nuclei (AGN) or quasars. These are found in large surveys of the sky. In this thesis, I use one of these surveys, the Hamburg/ESO survey (HES), to study the AGN population in the local volume (z~0). The demographics of AGN are traditionally represented by the AGN luminosity function, the distribution function of AGN at a given luminosity. I determined the local (z<0.3) optical luminosity function of so-called type 1 AGN, based on the broad band B_J magnitudes and AGN broad Halpha emission line luminosities, free of contamination from the host galaxy. I combined this result with fainter data from the Sloan Digital Sky Survey (SDSS) and constructed the best current optical AGN luminosity function at z~0. The comparison of the luminosity function with higher redshifts supports the current notion of 'AGN downsizing', i.e. the space density of the most luminous AGN peaks at higher redshifts and the space density of less luminous AGN peaks at lower redshifts. However, the AGN luminosity function does not reveal the full picture of active black hole demographics. This requires knowledge of the physical quantities, foremost the black hole mass and the accretion rate of the black hole, and the respective distribution functions, the active black hole mass function and the Eddington ratio distribution function. I developed a method for an unbiased estimate of these two distribution functions, employing a maximum likelihood technique and fully account for the selection function. I used this method to determine the active black hole mass function and the Eddington ratio distribution function for the local universe from the HES. I found a wide intrinsic distribution of black hole accretion rates and black hole masses. The comparison of the local active black hole mass function with the local total black hole mass function reveals evidence for 'AGN downsizing', in the sense that in the local universe the most massive black holes are in a less active stage then lower mass black holes. The second route I follow is a study of redshift evolution in the black hole-galaxy relations. While theoretical models can in general explain the existence of these relations, their redshift evolution puts strong constraints on these models. Observational studies on the black hole-galaxy relations naturally suffer from selection effects. These can potentially bias the conclusions inferred from the observations, if they are not taken into account. I investigated the issue of selection effects on type 1 AGN samples in detail and discuss various sources of bias, e.g. an AGN luminosity bias, an active fraction bias and an AGN evolution bias. If the selection function of the observational sample and the underlying distribution functions are known, it is possible to correct for this bias. I present a fitting method to obtain an unbiased estimate of the intrinsic black hole-galaxy relations from samples that are affected by selection effects. Third, I try to improve our census of dormant black holes and the determination of their masses. One of the most important techniques to determine the black hole mass in quiescent galaxies is via stellar dynamical modeling. This method employs photometric and kinematic observations of the galaxy and infers the gravitational potential from the stellar orbits. This method can reveal the presence of the black hole and give its mass, if the sphere of the black hole's gravitational influence is spatially resolved. However, usually the presence of a dark matter halo is ignored in the dynamical modeling, potentially causing a bias on the determined black hole mass. I ran dynamical models for a sample of 12 galaxies, including a dark matter halo. For galaxies for which the black hole's sphere of influence is not well resolved, I found that the black hole mass is systematically underestimated when the dark matter halo is ignored, while there is almost no effect for galaxies with well resolved sphere of influence.
Supermassereiche Schwarze Löcher sind ein fundamentaler Bestandteil unseres Universims im Allgemeinen, und von Galaxien im Besonderen. Fast jede massereiche Galaxie beherbergt ein supermassereiches Schwarzes Loch in seinem Zentrum. Außerdem existiert eine enge Beziehung zwischen dem Wachstum des Schwarzen Loches und der Entwicklung seiner umgebenden Galaxie. Diese zeigt sich besonders in der engen Beziehung zwischen der Masse eines Schwarzen Loches und den Eigenschaften der sphäroidalen Komponente der Galaxie, beispielsweise seiner stellaren Geschwindigkeitsdispersion, seiner Leuchtkraft und seiner Masse. Diese Beziehung erklären zu können, sowie das Wachstum von Schwarzen Löchern zu verstehen, liefert einen wichtigen Beitrag zu unserem Bild der Entstehung und Entwicklung von Galaxien. In dieser Arbeit steuere ich verschiedene Beiträge dazu bei unser Verständnis des Vorkommens Schwarzer Löcher und der Beziehung zu ihren Galaxien zu verbessern. Zunächst versuche ich ein vollständiges Bild der Anzahl und Eigenschaften Schwarzer Löcher zu erhalten. Dazu beschränke ich mich auf aktive Schwarze Löcher, wie man sie im Universum als Aktive Galaxienkerne (AGN) in großen Himmelsdurchmusterungen finden kann. Ich benutze eine solche Durchmusterung, das Hamburg/ESO Survey (HES), um die AGN Population im lokalen Universum zu studieren. Dazu habe ich die optische Leuchtkraftfunktion von AGN bestimmt. Diese habe ich mit anderen Ergebnissen leuchtschwächerer AGN kombiniert um die bisher beste AGN Leuchtkraftfunktion im lokalen Universum zu erhalten. Der Vergleich mit Ergebnissen bei höherer kosmischer Rotverschiebung bestätigt unser Bild des sogenannten "AGN downsizing". Dies sagt aus, dass leuchtkräftige AGN bei hoher Rotverschiebung am häufigsten vorkommen, während leuchtschwache AGN bei niedriger Rotverschiebung am häufigsten sind. Allerdings verrät uns die AGN Leuchtkraftfunktion allein noch nicht das ganze Bild der Demographie Schwarzer Löcher. Vielmehr sind wir an den zugrunde liegenden Eigenschaften, vor allem der Masse und der Akkretionsrate der Schwarzen Löcher, sowie deren statistischen Verteilungsfunktionen, interessiert. Ich habe eine Methode entwickelt um diese beiden Verteilungsfunktionen zu bestimmen, basierend auf der Maximum-Likelihood-Methode. Ich habe diese Methode benutzt um die aktive Massenfunktion Schwarzer Löcher, sowie die Verteilungsfunktion ihrer Akkretionsraten für das lokale Universum aus dem HES zu bestimmen. Sowohl die Akkretionsraten, als auch die Massen der Schwarzen Löcher zeigen intrinsisch eine breite Verteilung, im Gegensatz zur schmaleren beobachtbaren Verteilung. Der Vergleich der aktiven Massenfunktion mit der gesamten Massenfunktion Schwarzer Löcher zeigt ebenfalls Hinweise auf "AGN downsizing". Als nächstes habe ich mich mit Untersuchungen zur zeitlichen Entwicklung in den Beziehungen zwischen Schwarzem Loch und Galaxie beschäftigt. Diese kann helfen unser theoretisches Veständnis der physikalischen Vorgänge zu verbessern. Beobachtungen sind immer auch Auswahleffekten unterworfen. Diese können die Schlussfolgerungen aus den Beobachtungen zur Entwicklung in den Beziehungen beeinflussen, wenn sie nicht entsprechend berücksichtigt werden. Ich habe den Einfluss von Auswahleffekten auf AGN Stichproben im Detail untersucht, und verschiedende möchgliche Einflussquellen identifiziert, die die Beziehung verfälschen können. Wenn die Auswahlkriterien der Stichprobe, sowie die zugrunde liegenden Verteilungen bekannt sind, so ist es möglich für die Auswahleffekte zu korrigieren. Ich habe eine Methode entwickelt, mit der man die intrinsische Beziehung zwischem Schwarzem Loch und Galaxie aus den Beobachtungen rekonstruieren kann. Schließlich habe ich mich auch inaktiven Schwarzen Löchern und der Bestimmung ihrer Massen gewidmet. Eine der wichtigsten Methoden die Masse Schwarzer Löcher in normalen Galaxien zu bestimmen ist stellardynamische Modellierung. Diese Methode benutzt photometrische und kinematische Beobachtungen, und rekonstruiert daraus das Gravitationspotenzial aus der Analyse stellarer Orbits. Bisher wurde in diesen Modellen allerdings der Einfluss des Halos aus Dunkler Materie vernachlässigt. Dieser kann aber die Bestimmung der Masse des Schwarzen Loches beeinflussen. Ich habe 12 Galaxien mit Hilfe stellardynamischer Modellierung untersucht und dabei auch den Einfluss des Halos aus Dunkler Materie berücksichtigt. Für Galaxien bei denen der Einflussbereich des Schwarzen Loches nicht sehr gut räumlich aufgelöst war, wird die Masse des Schwarzen Loches systematisch unterschätzt, wenn der Dunkle Materie Halo nicht berücksichtigt wird. Auf der anderen Seite ist der Einfluss gering, wenn die Beobachtungen diesen Einflussbereich gut auflösen können.

This thesis concerns the use of observations of gravitational waves as tools for astronomy and fundamental physics. Gravitational waves are small ripples in spacetime produced by rapidly accelerating masses; their existence has been predicted for almost 100 years, but the first direct evidence of their existence came only very recently with the announcement in February 2016 of the detection by the LIGO and VIRGO collaborations. Part I of this thesis presents an introduction to gravitational wave astronomy, including a detailed discussion of a wide range of gravitational wave sources, their signal morphologies, and the experimental detectors used to observe them. Part II of this thesis concerns a particular data analysis problem which often arises when trying to infer the source properties from a gravitational wave observation. The use of an inaccurate signal model can cause significant systematic errors in the inferred source parameters. The work in this section concerns a proposed technique, called the Gaussian process marginalised likelihood, for overcoming this problem. Part III of this thesis concerns the possibility of testing if the gravitational field around an astrophysical black hole conforms to the predictions of general relativity and the cosmic censorship hypothesis. It is expected that the gravitational field should be well described by the famous Kerr solution. Two approaches for testing this hypothesis are considered; one using X-ray observations and one using gravitational waves. The results from these two approaches are compared and contrasted. Finally, the conclusions and a discussion of future prospects are presented in part IV of this thesis.

This thesis is conceptually divided into two parts. The first and main part concerns the generation of gravitational radiation that is emitted from merging black-hole binary systems using Numerical Relativity methods. The second part presents the methodology of the search for gravitational-wave bursts that are emitted in core-collapse Supernovae. My approach to Numerical Relativity is to utilise the late-time gravitational radiation of merging binary black holes to extract key astrophysical parameters from such systems via standard parameter estimation techniques. I begin with an introductory chapter that outlines the standard theories of stationary and perturbed black holes. In addition, up-to-date techniques in performing binary black hole simulations, the current and near-future status of the global network of gravitational-wave detectors, as well as the most promising gravitational-wave sources. I conclude the chapter with elements on parameter estimation techniques, such as Bayesian analysis and the Fisher information matrix. In Chapter 2, I discuss detection issues and parameter estimation results from the late-time radiation of colliding non-spinning black holes in quasi-circular orbits, and propose a practical test of General Relativity, as well as of the nature of the merged compact object. Chapter 3 involves similar parameter extraction calculations, but involves a more realistic approach, whereby the effect of the various angular parameters on parameter estimation is considered, placing an emphasis on the actual science benefit from measuring the gravitational radiation from perturbed intermediate and supermassive black holes. In Chapter 4 we present the results of an extensive Numerical Relativity study of merging spinning black hole binaries and argue that the mass ratio and individual spins of a non-precessing progenitor binary can be measured solely by observing the late-time radiation. Chapter 5 presents the methodology in carrying out searches for gravitationalwave bursts (GWB) from core-collapse Supernovae with a dedicated for GWB searches pipeline (X-Pipeline) and presents the sensitivity performance of XPipeline in detecting GWBs associated with certain Supernova candidates during the two most recent LIGO-Virgo-GEO Science Runs.

The main objective of this thesis is to understand from a microscopic point of view some of the characteristic phenomena of rotating black holes. The inclusion of rotation gives rise to physics that allows a more precise and detailed understanding of the microscopic string theory of black holes. In this thesis we focus on two models of particular interest: one is based on the D0-D6 system and the other on the D1-D5-P system. The former is interesting because, through its connection to M-theory, it yields a statistical-mechanics description of neutral black holes. The latter allows to have better control over the microscopic conformal field theory and yields a cleaner picture of the origin of superradiance. We extend the microscopic analysis of extremal dyonic Kaluza-Klein (D0-D6) black holes to cover the regime of fast rotation in addition to slow rotation. Fastly rotating black holes, incontrast to slow ones, have non-zero angular velocity and possess ergospheres, so they are more similar to the Kerr black hole. The D-brane model reproduces their entropy exactly, but the mass gets renormalized from weak to strong coupling, in agreement with recent macroscopic analyses of rotating attractors. We discuss how the microscopic model accounts for the fact that fastly rotating extremal KK black holes possess an ergosphere and exhibit superradiance while slow ones don't. In addition, we show in full generality how Myers-Perry black holes are obtained as a límit of Kaluza-Klein black holes, and discuss the slow and fast rotation regimes and superradiance in this context. A, perhaps surprising, consequence of our analysis is that both slowly and fastly-rotating KK black holes provide microscopic accounts of the entropy formula of MP black holes, even if they correspond to rather different microscopic states. As we discuss, this does not pose any problem, since the microscopic theory always retains a memory of how the 5D black hole is embedded within Taub-NUT. For a more detailed and quantitative study of black hole superradiance from the stringy microscopic side, we consider the D1-D5-P system. In order to disentangle superradiance from finite-temperature effects, we consider an extremal, rotating D1-D5-P black hole that has an ergosphere and is not supersymmetric. We explain how the microscopic dual accounts for the superradiant ergosphere of this black hole. The bound 0 < ω < mΩH on superradiant mode frequencies is argued to be a consequence of Fermi-Dirac statistics for the spin-carrying degrees of freedom in the dual CFT. We also compute the superradiant emission rates from both sides of the correspondence, and show their agreement. This is an extension of previous analyses of radiation from the D1-D5-P black holes. We generalize those results to include momentum for the bulk scalar. It would be interesting to extend our picture for superradiance to the smooth SUGRA solitons with D1-D5-P charges which correspond to CFT states such that both sectors are in pure states. Another issue to be investigated would be the absence of fermionic superradiance emission by the previously considered systems with ergoregion.
L'objectiu principal d'aquesta tesi és comprendre des d'un punt de vista microscòpic alguns dels fenòmens característics dels forats negres amb rotació. Ens centrem en forats negres amb rotació, extremals, però no supersimètrics. Aquesta mena de solucions són les més adequades per al nostre propòsit. A diferència del cas supersimètric, presenten una ergosfera i, per tant, s'hi pot produir el fenomen de la superradiància. Però, en tenir temperatura nul·la aquest fenomen no apareix “barrejat” amb la radiació de Hawking d'origen purament tèrmic. Alhora, aquestes geometries extremals també preserven el nombre de microestats en passar d'acoblament feble a acoblament fort. La primera part de la tesi, se centra en l'estudi microscòpic de l'entropia dels forats negres de Kaluza-Klein amb rotació. Aquesta família de solucions, presenta dos límits extremals: el de “rotació lenta” i el de “rotació ràpida”. Treballs anteriors ja havien aconseguit reproduir l'entropia del primer cas. Aquí, estenem aquest càlcul al límit extremal amb rotació ràpida. Alhora, mostrem que el fenomen de la superradiància es pot explicar de manera anàloga a la radiació de Hawking, en termes de dues excitacions que xoquen i provoquen l'emissió d'una corda tancada. En aquest cas, aquest mode emès té necessàriament un moment angular diferent de zero. A la segona part, ens centrem en aquesta interpretació microscòpica de la superradiància amb un tractament més quantitatiu. En aquest cas, considerem les solucions extremals no supersimètriques del sistema D1-D5-P amb rotació. A partir de la seva descripció microscòpica, aconseguim reproduir la condició de superradiància ω < mΩH i mostrem que es pot entendre com a conseqüència de l'estadística de Fermi-Dirac. També avaluem els ritmes d'emissió de superradiància des del punt de vista macroscòpic i microscòpic i analitzem si concorden.

We present a method for solving the Einstein-Maxwell equations in a five dimensional, asymptotically flat, black hole spacetime with three commuting Killing vector fields. In particular, we show that by reducing the dimension of the Einstein-Maxwell equations in a Kaluza-Klein like manner we can determine the components of the metric and vector potential which lie in the direction of the Killing vector fields. These components are determined by nine scalar fields each of which satisfy a partial differential equation in two variables. These equations take the form of an elliptic operator set equal to a nonlinear source. We find evidence that particular combinations of these fields satisfy Dirichlet boundary conditions, and are well suited to numerical solution using Green functions. Using this method we generate numerical solutions to the 4+1 Einstein-Maxwell equations corresponding to charged generalizations of the Myers-Perry solution. We also discover symmetry relations among the scalar equations which constrain their functional forms and posit the existence of two rigidity-theorem-like relations for electrovac spacetimes and sketch how their use generalizes our method to N+1 dimensions.

As they are evaporating, black holes are emitting radiations called Hawking radiations. Our goal is to determine at which distance it is possible to measure those radiations with current telescopes. Being capable of measuring those radiations would mean that we can use them as standard candles i.e. we could use it as distance indicator. To do so, we are  first going to compute the different characteristics of a black hole such as its energy peak, temperature,  flux and lifetime. Knowing that, we will be able to describe how, theoretically, we could use black holes as standard candles. Finally, we will take the Fermi-LAT telescope as an example of what we can observe in practice and at which distance.

Doctor of Philosophy
Department of Mathematics
Louis Crane
We exhibit a static, cylindrically symmetric, exact solution to the Euler-Heisenberg field equations (EHFE) and prove that its effective geometry contains (optical) black holes. It is conjectured that there are also soliton solutions to the EHFE which contain black hole geometries.

Radio galaxies and quasars are among the largest and most powerful single objects known and are believed to have had a significant impact on the evolving Universe and its large scale structure. Their jets inject a significant amount of energy into the surrounding medium, hence they can provide useful information in the study of the density and evolution of the intergalactic and intracluster medium. The jet activity is also believed to regulate the growth of massive galaxies via the AGN feedback. In this thesis I explore the intrinsic and extrinsic physical properties of the population of Fanaroff-Riley II (FR II) objects, i.e. their kinetic luminosities, lifetimes, and central densities of their environments. In particular, the radio and kinetic luminosity functions of these powerful radio sources are investigated using the complete, flux limited radio catalogues of 3CRR and BRL. I construct multidimensional Monte Carlo simulations using semi-analytical models of FR II source time evolution to create artificial samples of radio galaxies. Unlike previous studies, I compare radio luminosity functions found with both the observed and simulated data to explore the best-fitting fundamental source parameters. The Monte Carlo method presented here allows one to: (i) set better limits on the predicted fundamental parameters of which confidence intervals estimated over broad ranges are presented, and (ii) generate the most plausible underlying parent populations of these radio sources. Moreover, I allow the source physical properties to co-evolve with redshift, and I find that all the investigated parameters most likely undergo cosmological evolution; however these parameters are strongly degenerate, and independent constraints are necessary to draw more precise conclusions. Furthermore, since it has been suggested that low luminosity FR IIs may be distinct from their powerful equivalents, I attempt to investigate fundamental properties of a sample of low redshift, low radio luminosity density radio galaxies. Based on SDSS-FIRST-NVSS radio sample I construct a low frequency (325 MHz) sample of radio galaxies and attempt to explore the fundamental properties of these low luminosity radio sources. The results are discussed through comparison with the results from the powerful radio sources of the 3CRR and BRL samples. Finally, I investigate the total power injected by populations of these powerful radio sources at various cosmological epochs and discuss the significance of the impact of these sources on the evolving Universe. Remarkably, sets of two degenerate fundamental parameters, the kinetic luminosity and maximum lifetimes of radio sources, despite the degeneracy provide particularly robust estimates of the total power produced by FR IIs during their lifetimes. This can be also used for robust estimations of the quenching of the cooling flows in cluster of galaxies.

According to Einstein's theory of General Relativity, the acceleration of matter can cause ripples in the curvature of spacetime, given the name gravitational waves. Such ripples are negligible in magnitude for all but the most energetic astrophysical events, such as the coalescence of compact binary stars. In 2015, gravitational waves were first directly detected from a binary black hole (BBH) coalescence [19]. This was achieved using two independent laser interferometers which each measured the fluctuations caused by the gravitational waves as they passed by. Matched filtering and other data analysis techniques were then employed to identify the properties of the source and measure the likelihood that the detection is a false alarm. The efficacy of these matched filtering techniques is pivotal to not only detecting gravitational waves, but drawing as much information about their sources as possible. The methods for detecting a BBH involve the construction of a template bank; a group of synthesised waveforms which each represent a detectable series of gravitational waves that a BBH could produce. The characteristics of a BBH template are governed by the two masses and how they spin, the distance to the source, its orientation and its sky location. Current template banks do not include templates for sources where the spins are misaligned with the orbital momentum, which is the cause of precession in BBH. Thus, the algorithms are effective for detecting a non-precessing BBH, but much less sensitive towards precessing sources. Creating a template bank which includes all possible precessing waveforms is computationally infeasible and would induce enough statistical noise to negate any extra sensitivity gained. However, many precessing signals would be undetectable or indistinguishable from non-precessing signals. Including such signals in a bank would result in no gain in its sensitivity. This thesis attempts to locate areas of precessing parameter space where waveforms are distinguishable from non-precessing sources, and begins work on forming a function which maps observable precession through parameter space.

This thesis presents theoretical results on the tidal disruption of stars by supermassive black holes (SMBHs). The multiwavelength ares produced by tidal disruption events (TDEs) have supernova-like luminosities, and associated relativistic jets can be visible to cosmological distances. TDEs probe the demography of quiescent SMBHs, and are natural laboratories for jet launching mechanisms and super-Eddington accretion. The first chapter broadly surveys TDE physics. The second and third chapters estimate the TDE rate following gravitational wave (GW) recoil of a SMBH (after a SMBH binary merger). Immediately after GW recoil, the TDE rate increases, sometimes to \(~10^{-1}\) TDEs per year. This "burst" of TDE flares can provide an electromagnetic counterpart to low frequency GW signals, localizing sources and measuring cosmological parameters. Millions of years later, recoiled SMBHs wandering through their host galaxies will produce spatially offset TDEs at a rate which is likely detectable with the LSST. In the fourth chapter, we show that standard estimates for \(\Delta\epsilon\), the energy spread of TDE debris, are wrong, sometimes by orders of magnitude. Correcting this error reduces the observability of many TDEs. We introduce a new analytic model for tidal disruption, calculate \(\Delta\epsilon\)'s dependence on stellar spin, estimate general relativistic corrections to \(\Delta\epsilon\), and quantify the GW signal generated from tidal compression. The fifth chapter presents hydrodynamical simulations of TDE debris circularization, focusing on eccentric, rather than parabolic, orbits. General relativistic precession drives debris circularization, in contrast to past simulations using smaller black holes. In the sixth chapter, we show that TDE light curves can constrain or measure SMBH spins, as Lense-Thirring torques produce quasiperiodic variability in disk emission. Precession of a relativistic jet could also measure SMBH spin, and we apply our model to the relativistic Swift 1644+57 TDE. The seventh chapter considers the disruption of neutron stars (NSs) by stellar mass black holes (BHs) or other NSs. Jet precession in associated short-hard gamma ray bursts is uniquely possible for NS-BH (not NS-NS) mergers. We quantify typical precession amplitudes and periods, and calculate their time evolution. If disk viscosities are relatively low, electromagnetic observations alone could distinguish NS-BH from NS-NS mergers.
Astronomy

This thesis presents research into the X-ray binary population of NGC 5128 (Centaurus A). The two principle investigations focus on the identification of black hole candidates, which can be identified by their long term variability and spectral properties. We demonstrate this with what we believe is our best example; a source that faded over two months of observations and displayed cool disc thermal-dominant spectra when at high luminosities- similar to the Galactic black hole X-ray binaries. The main result of this research is that the population of black hole X-ray binaries is more pronounced in the dust lane of the galaxy compared to in the halo. The explanation of this result, based around the mass of the donor stars required for systems to emit at the observed luminosities, may also explain the long noted effect of a steepening of the X-ray luminosity function in early-type galaxies at a few 10٨38 erg/s; an effect that increases with the age of the stellar population. Finally, frequent Chandra observations of the NGC 5128 were used to investigate the two known ultraluminous X-ray sources. These are transient systems and were observed at luminosities (1-10)% of their peak, in the regime frequented by the Galactic X-ray binaries. This presented an exciting opportunity to study the lower luminosity behaviour of these systems in an effort to determine the mass of the accreting compact object. The results of the spectral analysis point towards accretion powered by a stellar, rather than intermediate mass black hole. The long term variability of these sources is reminiscent of several of the long period Galactic X-ray binaries.

The X-ray emission from accreting black holes provides the perfect probe for testing the geometry, behaviour and conditions present in the innermost regions of the accretion flow. In this thesis I use X-ray spectral analysis to investigate the properties of accreting black holes that extend over several orders of magnitude in accretion rate (m˙ E) and black hole mass (MBH), from the stellar mass black holes in X-ray binary systems (XRBs)to the supermassive black holes in active galactic nuclei(AGN). Firstly, through a survey of X-ray emission in the nuclei of nearby galaxies I show that the usefulness of the X-ray to optical line ratios as a Compton-thick diagnostic does not extend to low luminosity AGN, and instead these ratios may have more practical use in distinguishing between AGN and non-AGN emission processes. Secondly, and more importantly, the main focus of this thesis is upon the variability of the Comptonised power-law X-ray spectral component, and more specifically an examination of how the photon index

To constrain the era when the first galaxies and stars appeared upcoming instruments will rely on the brightest events in the universe: supernovae and brilliant emission from massive black holes. In this dissertation, we investigate the observability of certain types of supernovae of the very first stars (Population III stars) and find that while these events are sufficiently luminous to be observed with deep-sky instruments such as the James Webb Space Telescope (JWST), they may not observe these particular types of events in their lifetimes. We next explore the origins of massive black holes and introduce the direct collapse hypothesis of supermassive black hole formation. We model CR7, an apparently metal-free, luminous, Lyman-alpha emitting galaxy, as if it were powered by a massive direct collapse black hole and find that such a black hole can account for CR7's impressive Lyman-alpha flux. We finally investigate the nature of the connection between water megamasers, very bright radio sources originating from population inversion in dense, shocked gas around massive black holes and hydroxyl megamasers which generally accompany star formation. We carry out a ~ 60 hour radio survey for water emission among galaxies hosting OH megamaser hosts to assess the connection between the two types of emission. We find marginally statistically significant evidence that OH megamasers exclude water kilomasers and confirm with high levels of significance (> 8 sigma) the presence of a water megamaser in II Zw 96, establishing this object as the second galaxy known to cohost simultaneous water and hydroxyl megamasers.

The magnetic field dynamo in the inner part of accretion disks around supermassive black holes in AGNs may be an important mechanism for the generation of magnetic fields in galaxies and in extragalactic space. We consider dynamo with the necessary helicity generation produced by star-disk collisions. Gas heated by a star passing through the disk is buoyant and form rising and expanding plume of plasma. Due to Coriolis forces the flow produced by plumes have coherent helicity. This helicity is the source of alpha effect in the alpha-O dynamo in differentially rotating accretion disk. We apply the mean field dynamo theory to the ensemble of plumes produced by star-disk collisions. We demonstrate the existence of the dynamo and evaluate the growth rate of magnetic field. The estimate of the nonlinear saturated state of the dynamo gives the magnetic field exceeding equipartition with the thermal energy in the accretion disk. Thus, star-disk collision dynamo can be important in generating dynamically significant magnetic fields, which could alter the disk structure and be the source of the energy flow in extragalactic jets. We present results of numerical simulations of the kinematic dynamo produced by star-disk collisions. It was found that for about one star-disk collision per period of rotation of the inner edge of an accretion disk, the typical value of the threshold magnetic Reynolds number is of the order of 100. The generated mean magnetic field has predominantly even parity. We also present theoretical consideration of magnetic dynamo in New Mexico dynamo experiment, which is currently under construction. The experiment utilizes Couette flow and driven jets of liquid sodium to simulate astrophysical alpha-O dynamos in the laboratory. We perform numerical simulations with ideally conducting boundary and evaluate the changes, which vacuum boundary conditions introduce in our numerical results. We also develop the theory of the MHD Ekman boundary layer in differentially rotating conducting fluid. The Ekman layer is formed at the end plates in the experiment. We show that the Ekman layer does not influence the generation of the large scale magnetic field in the experiment.

Extensions to general relativity are often considered as possibilities in the quest for a quantum theory of gravity on one hand, or to resolve anomalies within cosmology on the other. Scalar fields, found in many areas of physics, are frequently studied in this context. This is partly due to their manifestation in the effective four dimensional theory of a number of underlying fundamental theories, most notably string theory. This thesis is concerned with the effects of scalar fields on cosmological and black hole solutions. By comparison, an analysis of an inhomogeneous cosmological model which requires no extensions to general relativity is also undertaken. In chapter three, examples of numerical solutions to black hole solutions, which have previously been shown to be linearly stable, are found. The model includes at least two scalar fields, non-minimally coupled to electromagnetism and hence possesses non-trivial contingent primary hair. We show that the extremal solutions have finite temperature for an arbitrary coupling constant. Chapter four investigates the effects of higher order curvature corrections and scalar fields on the late-time cosmological evolution. We find solutions which mimic many of the phenomenological features seen in the post-inflation Universe. The effects due to non-minimal scalar couplings to matter are also shown to be negligible in this context. Such solutions can be shown to be stable under homogeneous perturbations. Some restrictions on the value of the slope of the scalar coupling to the Gauss-Bonnet term are found to be necessary to avoid late-time superluminal behaviour and dominant energy condition violation. A number of observational tests are carried out in chapter five on a new approach to averaging the inhomogeneous Universe. In this "Fractal Bubble model" cosmic acceleration is realised as an apparent effect, due to quasilocal gravitational energy gradients. We show that a good fit can be found to three separate observations, the type Ia supernovae, the baryon acoustic oscillation scale and the angular scale of the sound horizon at last scattering. The best fit to the supernovae data is χ² ≃ 0:9 per degree of freedom, with a Hubble parameter at the present epoch of H0 = 61:7+1:4 -1:3 km sec⁻¹ Mpc⁻¹ , and a present epoch volume void fraction of 0:76 ± 0:05.

Thesis (Ph. D.)--University of Oregon, 2006.
Typescript. Includes vita and abstract. Includes bibliographical references (leaves 75-80). Also available for download via the World Wide Web; free to University of Oregon users.

However successful classical general relativity is, it faces non-normalizability problems at the quantum mechanical level. Nevertheless, it predicts the existence of black holes, which are thermal objects that are expected to still exist in a satisfactory theory of quantum gravity. This is one of the main reasons why black holes are important. String theory is considered, today, to be the most successful candidate for a quantum theory of gravity. Its mathematical consistency requires spacetime to have ten dimensions, and thus, it motivates the study of general relativity, and in particular, black holes, in higher dimensions. This is the main focus of our thesis. Moreover, the advent of the AdS/CFT correspondence, relating a theory of gravity to a quantum field theory in one less dimension have raised even more the interest in higher dimensional gravity. Compared to four-dimensional general relativity, which has been largely studied and investigated in the past years, general relativity in higher dimensions has many interesting and new features. Uniqueness is one property of four dimensional general relativity that does not continue to hold in higher dimensions. Another related property is that in four dimensions black holes can have horizons of a spherical topology only, while in higher dimensions black objects can have other topologies as well. Black rings are a manifestation of this. The last two new properties lead to topological phase transitions in the phase space of higher dimensional black holes, which is one of the topics we consider and touch upon in this thesis. The existence of extended black objects in higher dimensions, called black “p”-branes, is an important and fundamental issue. Those objects were found to be dynamically unstable. Therefore, the following of this instability has become an important problem. What is the end state of it?. This instability is known as the Gregory-Laamme instability and it is another topic we investigate in our thesis and which we relate to a type of fluid-gravity correspondence in at spacetime. The existence of black “p”-branes is attributed to the fact that in higher dimensional general relativity there are black holes that can rotate as fast as one wishes. That is, there is no analogue of the four-dimensional Kerr bound which prevents black holes from spinning very fast. The fast rotation, on the other hand, which is possible in higher dimensions has the effect that it makes the horizon of the black hole flattens along the rotation plane, and hence, in the limit it approaches the black “p”-brane geometry. In chapter [3] we give a short introduction to the blackfolds approach to higher dimensional black holes. We discuss the reasons that make new approximate methods available in higher dimensions. We introduce the basic objects, or the building blocks, of the approach, which are the boosted black “p”-branes, and explain how the blackfolds approach can be used to construct from them new stationary solutions to the gravitational field equations with new and novel topologies and how it can be used to construct dynamical solutions as well. In chapter [4] we give a brief introduction to the topic of topology change in general relativity. We discuss the Kaluza-Klein black hole phases, the homogeneous black string phase, the inhomogeneous black string phase and the localized black hole phase. We explain the mechanism under which a topological phase transition appears as one moves in the phase space from a black string to a localized black hole. In chapter [5] we managed to formulate a type of fluid-gravity correspondence in at space. We found a map between a fluctuating boosed black “p”-brane and a relativistic viscous fluid living at spatial infinity. That is, we constructed a solution to the vacuum Einstein equations of a dynamical black “p”-brane up to first order in derivatives. The dual viscous fluid is characterized by two parameters (transport coefficients) in the stress tensor - the shear and bulk viscosities. Using the gravitational solution we succeeded to compute those coefficients. Furthermore, by using the effective description of the black “p”-brane as a viscous fluid in a lower number of dimensions we studied the Gregory-Laamme instability and we found a striking agreement with the numerical results, already obtained, on this problem (which were obtained by analyzing the linearized gravitational equations). In more details, by including the damping effect of the viscosity in the unstable sound waves, we obtained a remarkably good and simple approximation to the dispersion relation of the Gregory-Laamme modes, whose accuracy increases with the number of transverse dimensions. We proposed an exact limiting form as the number of dimensions tends to infinity. Hence, instead of attacking the complicated (linearized) gravitational equations we propose instead to attack the relativistic Navier-Stokes equations of the effective (dual) fluid, as they are much simpler than the former. In chapter [6] we tackled and made progress in a different problem - topology change in higher dimensional general relativity. Before the advent of our work there had been no analytical (but only numerical) complete example of a topological phase transition in general relativity. The black string / black hole phase transition in Kaluza-Klein spaces was analyzed and studied only numerically. Neverthelss, some local models had been obtained analytically. It was argued that the phase transition passes through (or is mediated by) a singular critical configuration; a self-similar double cone geometry. This geometry was found only locally, though. In our work we have provided for the first time a complete analytical example of a topological phase transition. We took the rotating black hole inside de-Sitter space (the Kerr-de-Sitter black hole), and we showed that if one follows a trajectory in the phase space of solutions along which the black hole rotation is increased then it will pancake along the rotation plane, and finally it will touch the de-Sitter horizon along that plane. A merger transition is obtained if one continues to move along the same phase space trajectory, leading to a merged phase with a single connected horizon. In our example, the critical configuration (in which the two horizons just meet) is mediated by a self-similar double cone, thus confirming previous propositions of the mechanism under which topological transitions work. We also described local models for the critical geometries that control many transitions in the phase space of higher-dimensional black holes, such as the pinch-down of a topologically spherical black hole to a black ring or to a black p-sphere, or the merger between black holes and black rings in black Saturns or di-rings in D >/= 6. It is worth mentioning, in addition, that the cones we have found are general ones (compared to previously known ones), in the sense that they describe two horizons that intersect each other at different temperatures, not only ones that intersect each other with the same temperature. However, in the case the two horizons intersect at different temperatures, there can be no merger transition afterwards, and so the trajectory of solutions in the phase space ends there.
Malgrat el seu èxit a nivell clàssic, la relativitat general s'enfronta a problemes de no-renormalitzabilitat a nivell quàntic. No obstant, prediu l'existència de forats negres, que són objectes tèrmics que s'espera que continuïin existint en una teoria satisfactòria de gravetat quàntica. La seva consistència matemàtica requereix que l'espai-temps tingui deu dimensions, i d'aquesta manera motiva l'estudi de la relativitat general, i en particular els forats negres, en dimensions altes. Aquest és el tema central de la nostra tesi. A més, l'adveniment de la correspondència AdS/CFT, que relaciona una teoria de gravetat amb una teoria quàntica de camps en una dimensió menys, ha incrementat encara més l'interès en la gravetat en dimensions altes. Comparada amb la relativitat general en quatre dimensions, que ha estat àmpliament estudiada i investigada els darrers anys, la relativitat general en dimensions més altes té moltes característiques noves i interessants. La unicitat és una propietat de la relativitat general en quatre dimensions que no continua sent vàlida en dimensions més altes. Una altra propietat relacionada amb aquesta és que en quatre dimensions els forats negres només poden tenir horitzons amb topologia esfèrica, mentre que en dimensions més altes els objectes negres poden tenir també altres topologies. Els anells negres són una manifestació d'això. Les dues noves propietats esmentades donen lloc a transicions de fase topològiques a l'espai de fases dels forats negres en dimensions altes, que és un dels temes que considerem i als quals contribuïm en aquesta tesi. L'existència d'objectes negres estesos en dimensions altes, anomenats p-branes negres, és un tema important i fonamental. Se sap que aquests objectes són dinàmicament inestables. Per tant, la qüestió de cap on condueix aquesta inestabilitat ha esdevingut un problema important. Quin és l'estat final? Aquesta inestabilitat es coneix com la inestabilitat de Gregory-Laflamme i és un altre tema que investiguem a la nostra tesi, i que relacionem amb un tipus de correspondència entre fluids i gravetat a l'espai-temps pla. L'existència de p-branes negres s'atribueix al fet que en relativitat general en dimensions altes hi ha forats negres que poden rotar de manera arbitràriament ràpida. és a dir, no hi ha un anàleg de la cota de Kerr en quatre dimensions, que impedeix que els forats negres donin voltes molt de pressa. La rotació ràpida, per altra banda, que és possible en dimensions més altes té l'efecte d'aplanar l'horitzó del forat negre al llarg del pla de rotació, i per tant en el limit de velocitats altes s'apropa a la geometria de la p-brana negra. Al capítol 3 donem una breu introducció a l'estudi de forats negres en dimensions més altes per mitjà de les anomenades ``blackfolds''. Discutim les raons per les quals hom pot fer servir nous mètodes aproximats en dimensions més altes. Introduïm els objectes bàsics de l'enfoc amb blackfolds, les p-branes negres impulsades, i expliquem com l'enfoc amb blackfolds es pot fer servir per construir a partir d'elles noves solucions estacionàries de les equacions del camp gravitatori amb noves topologies, i com es pot fer servir també per construir solucions dinàmiques. Al capítol 4 donem una breu introducció al tema dels canvis de topologia en relativitat general. Discutim les fases del forat negre de Kaluza-Klein, la fase de corda negra homogènia, la fase de corda negra inhomogènia i fase de forat negre localitzat. Expliquem el mecanisme pel qual apareix una transició de fase topològica quan hom es mou per l'espai de fases des d'una corda negra fins a un forat negre localitzat. Al capítol 5 hem aconseguit formular un tipus de correspondència entre fluids i gravetat a l'espai pla. Hem trobat un mapa entre una p-brana negra impulsada fluctuant i un fluid viscós relativista situat a l'infinit espacial. és a dir, hem constrïit una solució de les equacions d'Einstein al buit d'una p-brana negra dinàmica fins a primer ordre en derivades. El fluid viscós dual està caracteritzat per dos paràmetres (coeficients de transport) al tensor d'energia-moment, la viscositat de cisallament i la viscositat de compressió. Fent servir la solució gravitatória hem pogut calcular aquests coeficients. A més, fent servir la descripció efectiva de la p-brana negra com un fluid viscós en un nombre més baix de dimensions hem estudiat la inestabilitat de Gregory-Laflamme, i els nostres resultats estan d'acord de manera molt precisa amb els resultats numèrics prèviament obtinguts en aquest problema (que havien estat obtinguts per mitjà d'una anàlisi de les equacions gravitaòóries linealitzades). Més en detall, incloent l'efecte d'amortiment de la viscositat en les ones de so inestables hem obtingut una aproximació remarcablement bona i senzilla a la relació de dispersió dels modes de Gregory-Laflamme, la precisió de la qual augmenta amb el nombre de dimensions transverses. Hem proposat una forma límit exacta quan el nombre de dimensions tendeix a infinit. Així, en lloc d'intentar resoldre les complicades equacions gravitatòries (linealitzades) proposem intentar resoldre les equacions relativistes de Navier-Stokes per al fluid efectiu (dual), ja que aquestes són molt més senzilles que les primeres. Al capítol 6 hem abordat i hem fet progrés en un altre problema: canvi de topologia en relativitat general en dimensions més altes. Abans del nostre treball no hi havia cap exemple analític complet (només n'hi havia de numèrics) d'una transició de fase topològica en relativitat general. La transició de fase corda negra/ forat negre en espais de Kaluza-Klein havia estat analitzada i estudiada només numèricament. No obstant, alguns models locals

Thesis (Ph. D.)--Ohio State University, 2004.
Title from first page of PDF file. Document formatted into pages; contains xii, 287 p.; also includes graphics. Includes bibliographical references (p. 279-287).