Academic literature on the topic 'Relativity and gravitational theory – General relativity – Black holes'

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Journal articles on the topic "Relativity and gravitational theory – General relativity – Black holes"

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Barausse, Enrico. "Black Holes in General Relativity and Beyond." Proceedings 17, no. 1 (June 14, 2019): 1. http://dx.doi.org/10.3390/proceedings2019017001.

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The recent detections of gravitational waves from binary systems of black holes are in remarkable agreement with the predictions of General Relativity. In this pedagogical mini-review, I go through the physics of the different phases of the evolution of black hole binary systems, providing a qualitative physical interpretation of each one of them. I also briefly describe how these phases would be modified if gravitation were described by a theory extending or deforming General Relativity, or if the binary components turned out to be more exotic compact objects than black holes.
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Yadav, Ranjit Prasad. "Theory of General Relativity: Historical Perspective." Academic Voices: A Multidisciplinary Journal 4 (March 28, 2015): 49–52. http://dx.doi.org/10.3126/av.v4i0.12358.

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General relativity was developed by Albert Einstein near about 100 Years ago. This article attempt to give an outline about the brief history of general theory of relativity and to understand the background to the theory we have to look at how theories of gravitation developed. Before the advent of GR, Newton's law of gravitation had been accepted for more than two hundred years as a valid description of the gravitational force between masses i.e. gravity was the result of an attractive force between massive objects. General relativity has developed in to an essential tool in modern astrophysics. It provides the foundation for the understanding of black holes, regions of space where gravitational attraction is strong that not even light can escape and also a part of the big bang model of cosmology.DOI: http://dx.doi.org/10.3126/av.v4i0.12358Academic Voices Vol.4 2014: 49-52
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Will, Clifford M. "The confrontation between general relativity and experiment." Proceedings of the International Astronomical Union 5, S261 (April 2009): 198–99. http://dx.doi.org/10.1017/s174392130999038x.

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AbstractWe review the experimental evidence for Einstein's general relativity. A variety of high precision null experiments confirm the Einstein Equivalence Principle, which underlies the concept that gravitation is synonymous with spacetime geometry, and must be described by a metric theory. Solar system experiments that test the weak-field, post-Newtonian limit of metric theories strongly favor general relativity. Binary pulsars test gravitational-wave damping and aspects of strong-field general relativity. During the coming decades, tests of general relativity in new regimes may be possible. Laser interferometric gravitational-wave observatories on Earth and in space may provide new tests via precise measurements of the properties of gravitational waves. Future efforts using X-ray, infrared, gamma-ray and gravitational-wave astronomy may one day test general relativity in the strong-field regime near black holes and neutron stars.
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Ahmed, Shohel, and Md Showkat Ali. "Numerical Relativity: Solving Geodesics equation for Massive Particle Around Black Holes Horizon." GANIT: Journal of Bangladesh Mathematical Society 35 (June 28, 2016): 79–85. http://dx.doi.org/10.3329/ganit.v35i0.28571.

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General relativity is the most beautiful physical theory ever invented. It describes one of the most pervasive features of the world we experience - gravitation. The gravitational field acts on nearby matter defines by the curvature of space-time. The black holes of nature are the most perfect macroscopic objects there are in the universe that constructed our concept of space-time. In this paper we use Einstein’s general relativity to model the motions of massive particles around the two black holes: static and rotating. These equations of motion around black holes will be studied with special focus towards the variation of symmetry by the change of gravitational effect.GANIT J. Bangladesh Math. Soc.Vol. 35 (2015) 79-85
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HOD, SHAHAR. "A SIMPLIFIED TWO-BODY PROBLEM IN GENERAL RELATIVITY." International Journal of Modern Physics D 22, no. 12 (October 2013): 1342029. http://dx.doi.org/10.1142/s0218271813420297.

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General relativity, Einstein's theory of gravity, predicts a universe full of black holes and gravitational waves. The prospects of detecting gravitational waves from inspirals of compact astrophysical objects into supermassive black holes have made it highly important to analyze in detail the gravitational two-body problem. While the two-body problem in Newtonian gravity (the weak-field limit) has a well-defined compact analytic solution, the corresponding problem in general relativity (the strong-field regime) is very complex and cannot be solved analytically. In this paper, we propose to model the two-body problem in general relativity using the analytically solvable model of a ring of particles in orbit around a central black hole. We use our model to calculate the innermost stable circular orbit (ISCO) frequency which characterizes the two-body dynamics. Remarkably, our expression for the characteristic ISCO frequency through linear order in the ring's mass predicts with astonishing accuracy the actual value of this fundamental parameter.
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Lo, C. Y. "The question on the existence of black holes." Physics Essays 34, no. 4 (December 1, 2021): 464–69. http://dx.doi.org/10.4006/0836-1398-34.4.464.

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Simulation shows that general relativity would lead to the existence of black holes if gravitation is always attractive. However, although we observed an invisible and extremely heavy object governs the orbits of stars at the center of our galaxy, we still cannot determine the existence of a black hole. Thus, one may ask whether black holes actually exist. Einstein’s general relativity has been established, because its prediction on the bending of light rays has been confirmed by observation. However, Einstein’s prediction on the increment of weight for a piece of metal as the temperature increases is proven incorrect by experiments, which actually show a reduction of weight. This leads to the necessary existence of repulsive gravitational force, which has been demonstrated by a charged capacitor hovering above the earth. Thus, Einstein, Newton, Galileo, and Maxwell all made the error of overlooking the repulsive gravitational charge-mass interaction. Thus, it is necessary to rejustify the existence of black holes, because gravity is not always attractive. Moreover, repulsive gravitational force makes it necessary to extend general relativity to a five-dimensional theory. Thus, to find out whether black holes exist, it is necessary to investigate the repulsive gravitation and a five-dimensional space.
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Shankaranarayanan, S. "Strong gravity signatures in the polarization of gravitational waves." International Journal of Modern Physics D 28, no. 14 (October 2019): 1944020. http://dx.doi.org/10.1142/s0218271819440206.

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General Relativity is a hugely successful description of gravitation. However, both theory and observations suggest that General Relativity might have significant classical and quantum corrections in the Strong Gravity regime. Testing the strong field limit of gravity is one of the main objectives of the future gravitational wave detectors. One way to detect strong gravity is through the polarization of gravitational waves. For quasi-normal modes of black-holes in General Relativity, the two polarization states of gravitational waves have the same amplitude and frequency spectrum. Using the principle of energy conservation, we show that the polarizations differ for modified gravity theories. We obtain a diagnostic parameter for polarization mismatch that provides a unique way to distinguish General Relativity and modified gravity theories in gravitational wave detectors.
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Eisenstaedt, Jean. "Dark Bodies and Black Holes, Magic Circles and Montgolfiers: Light and Gravitation from Newton to Einstein." Science in Context 6, no. 1 (1993): 83–106. http://dx.doi.org/10.1017/s0269889700001320.

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The ArgumentThe question of the possible existence of black holes is closely related to the question of the action of gravitation on the propagation of light. It has been raised recurrently from the when that Newton referred to a possible bending of light in his Opticks. And it relies on apparently simple questions: Is light subject to gravitation? What is the effect of a gravitational field on the propagation of light? Could a particle of light emitted by a star be retained by its gravitational field?From the end of the 1960s, the black hole idea has had a very important place in the relativistic literature, not to speak of the popularization of the theory. It turned out to be not only an important concept but also a tool that permitted us to understand general relativity better, indeed a tool that contributed greatly to changing the interpretation of Einstein's theory of gravitation. Here too I want to use this concept of the black hole to assist our understanding of the history of general relativity: the black hole is a fundamental milestone in the evolution of general relativity.
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Nashed, Gamal. "Charged and Non-Charged Black Hole Solutions in Mimetic Gravitational Theory." Symmetry 10, no. 11 (November 1, 2018): 559. http://dx.doi.org/10.3390/sym10110559.

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In this study, we derive, in the framework of mimetic theory, charged and non-charged black hole solutions for spherically symmetric as well as flat horizon spacetimes. The asymptotic behavior of those black holes behave as flat or (A)dS spacetimes and coincide with the solutions derived before in general relativity theory. Using the field equations of non-linear electrodynamics mimetic theory we derive new black hole solutions with monopole and quadrupole terms. The quadruple term of those black holes is related by a constant so that its vanishing makes the solutions coincide with the linear Maxwell black holes. We study the singularities of those solutions and show that they possess stronger singularity than the ones known in general relativity. Among many things, we study the horizons as well as the heat capacity to see if the black holes derived in this study have thermodynamical stability or not.
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Thorne, Kip S. "Gravitational Waves from Compact Bodies." Symposium - International Astronomical Union 165 (1996): 153–83. http://dx.doi.org/10.1017/s0074180900055649.

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According to general relativity theory, compact concentrations of energy (e.g., neutron stars and black holes) should warp spacetime strongly, and whenever such an energy concentration changes shape, it should create a dynamically changing spacetime warpage that propagates out through the Universe at the speed of light. This propagating warpage is called gravitational radiation — a name that arises from general relativity's description of gravity as a consequence of spacetime warpage.
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Dissertations / Theses on the topic "Relativity and gravitational theory – General relativity – Black holes"

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McManus, Ryan. "Testing gravity in the local universe." Thesis, University of Edinburgh, 2018. http://hdl.handle.net/1842/33214.

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General relativity (GR) has stood as the most accurate description of gravity for the last 100 years, weathering a barrage of rigorous tests. However, attempts to derive GR from a more fundamental theory or to capture further physical principles at high energies has led to a vast number of alternative gravity theories. The individual examination of each gravity theory is infeasible and as such a systematic method of examining modified gravity theories is a necessity. Studying generic classes of gravity theories allows for general statements about observables to be made independent of explicit models. Take, for example, those models described by the Horndeski action, the most general class of scalar-tensor theory with at most second-order derivatives in the equations of motion, satisfying theoretical constraints. But these constraints alone are not enough for a given modified gravity model to be physically viable and hence worth studying. In particular, observations place incredibly tight constraints on the size of any deviation in the solar system. Hence, any modified gravity would have to mimic GR in such a situation. To accommodate this requirement, many models invoke screening mechanisms which suppress deviations from GR in regions of high density. But these mechanisms really upon non-linear effects and so studying them in complex models is mathematically complex. To constrain the space of actions of Horndeski type to those which pass solar-system tests, a set of conditions on the four free functions of the Horndeski action are derived which indicate whether a specific model embedded in the action possesses a GR limit. For this purpose, a new and surprisingly simple scaling method is developed, identifying dominant terms in the equations of motion by considering formal limits of the couplings that enter through the new terms in the modified gravity action. Solutions to the dominant terms identify regimes where nonlinear terms dominate and Einstein's field equations are recovered to leading order. Together with an efficient approximation of the scalar field profile, one can determine whether the recovery of Einstein's field equations can be attributed to a genuine screening effect. The parameterised post-Newtonian (PPN) formalism has enabled stringent tests of static weak-field gravity in a theory-independent manner. This is through parameterising common perturbations of the metric found when performing a post-Newtonian expansion. The framework is adapted by introducing an effective gravitational coupling and defining the PPN parameters as functions of position. Screening mechanisms of modified gravity theories can then be incorporated into the PPN framework through further developing the scaling method into a perturbative series. The PPN functions are found through a combination of the scaling method with a post-Newtonian expansion within a screened region. For illustration, we show that both a chameleon and cubic galileon model have a limit where they recover GR. Moreover, we find the effective gravitational constant and all PPN functions for these two theories in the screened limit. To examine how the adapted formalism compares to solar-system tests, we also analyse the Shapiro time delay effect for these two models and find no deviations from GR insofar as the signal path and the perturbing mass reside in a screened region of space. As such, tests based upon the path light rays such as those done by the Cassini mission do not constrain these theories. Finally, gravitational waves have opened up a new regime where gravity can be tested. To this end, we examine how the generation of gravitational waves are affected by theories of gravity with screening to second post-Newtonian (PN) order beyond the quadrupole. This is done for a model of gravity where the black hole binary lies in a screened region, while the space between the binary's neighbourhood and the detector is described by Brans-Dicke theory. We find deviations at both 1.5 and 2 PN order. Deviations of this size can be measured by the Advanced LIGO gravitational wave detector highlighting that our calculation may allow for constraints to be placed on these theories. We model idealised data from the black hole merger signal GW150914 and perform a best fit analysis. The most likely value for the un-screened Brans-Dicke parameter is found to be ω = -1:42, implying on large scales gravity is very modified, incompatible with cosmological results.
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Echeverria, Fernando Thorne Kip S. "Topics in general relativity theory : gravitational-wave measurements of black-hole parameters ; gravitational collapse of a cylindrical body ; and classical-particle evolution in the presence of closed, timelike curves /." Diss., Pasadena, Calif. : California Institute of Technology, 1993. http://resolver.caltech.edu/CaltechETD:etd-12082008-095402.

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Pozzoli, Valentina. "Environnements gravitationnels, flots et fluides holographiques." Phd thesis, Ecole Polytechnique X, 2013. http://pastel.archives-ouvertes.fr/pastel-00915148.

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Différents environnements gravitationnels à 4 dimensions sont abordés dans ce thése : instantons gravitationnels et trous noirs aussi bien en relativité générale qu'en supergravité. La recherche de nouvelles solutions en relativité est un véritable défi. Cette tâche est nettement simplifiée dans l'hypothèse où l'on dispose d'un tenseur de Riemann auto-dual. Ces solutions sont dites instantons gravitationnels. L'évolution des instantons est décrite par un flot géométrique. Ce lien est analysé en détail, en focalisant l'attention sur le rôle du tensor de Ricci dans le flot géométrique. En espace de type Anti-de-Sitter (AdS), trouver de nouveaux trous noirs avec symétrie axiale est une question toujours ouverte. Cette question peut être posée dans le contexte des fluides holographiques. Trous noirs en rotation correspondent à des fluides aux vorticités particulières. En imposant que la solution soit régulière sur l'horizon, le fluide acquiert la forme d'un fluide parfait. Des conditions nécessaires afin que la correspondence entre solution gravitationnelle et théorie hydrodynamique, qui se fait usuellement par un développement perturbatif, puisse être ressommé et pour qu'on puisse trouver des solutions exactes de la relativité ont etées trouvées. Le comptage de l'entropie des trous noirs dans des espaces AdS ne fait toujours pas partie des résultats connus. Dans le cas des solutions en rotation des théories de supergravité N=2, une relation entre trous noirs extremaux non-BPS en espace plat et trous noirs BPS en espace AdS a été mise au point. La connexion entre cettes solutions donne des informations sur le comptage microscopique.
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Moore, Christopher James. "Gravitational waves : understanding black holes." Thesis, University of Cambridge, 2016. https://www.repository.cam.ac.uk/handle/1810/257043.

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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.
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Kim, Yunho. "Quadratic Gravity with Black Holes and Gravitational Waves." Thesis, The University of Sydney, 2021. https://hdl.handle.net/2123/26707.

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This thesis investigates black holes and gravitational waves in the framework of quadratic gravity. These subjects are introduced by first examining the current state of general relativity and how it is realised. The discussion then addresses the quantitative aspects of black holes, gravitational waves, and quadratic gravity. This is then followed by the exploration of the three main research topics. The first research topic investigates the induced charging of a black hole due to a topological term in quadratic gravity. The second research topic focuses on the approximate analytic non-Schwarzschild black hole solutions in quadratic gravity. Finally, gravitational waves generated by binary systems within quadratic gravity are studied, with a focus on the corrections produced by the massive scalar field and the massive spin-2 field.
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Chua, Alvin J. K. "Topics in gravitational-wave astronomy : theoretical studies, source modelling and statistical methods." Thesis, University of Cambridge, 2017. https://www.repository.cam.ac.uk/handle/1810/263652.

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Astronomy with gravitational-wave observations is now a reality. Much of the theoretical research in this field falls under three broad themes: the mathematical description and physical understanding of gravitational radiation and its effects; the construction of accurate and computationally efficient waveform models for astrophysical sources; and the improved statistical analysis of noisy data from interferometric detectors, so as to extract and characterise source signals. The doctoral thesis presented in this dissertation is an investigation of various topics across these themes. Under the first theme, we examine the direct interaction between gravitational waves and electromagnetic fields in a self-contained theoretical study; this is done with a view to understanding the observational implications for highly energetic astrophysical events that radiate in both the gravitational and electromagnetic sectors. We then delve into the second theme of source modelling by developing and implementing an improved waveform model for the extreme-mass-ratio inspirals of stellar-mass compact objects into supermassive black holes, which are an important class of source for future space-based detectors such as the Laser Interferometer Space Antenna. Two separate topics are explored under the third theme of data analysis. We begin with the procedure of searching for gravitational-wave signals in detector data, and propose several combinatorial compression schemes for the large banks of waveform templates that are matched against putative signals, before studying the usefulness of these schemes for accelerating searches. After a gravitational-wave source is detected, the follow-up process is to measure its parameters in detail from the data; this is addressed as we apply the machine-learning technique of Gaussian process regression to gravitational-wave data analysis, and in particular to the formidable problem of parameter estimation for extreme-mass-ratio inspirals.
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Pozzoli, Valentina. "Gravitational environments, flows and holographic fluids." Palaiseau, Ecole polytechnique, 2013. http://pastel.archives-ouvertes.fr/docs/00/91/51/48/PDF/Pozzoli.pdf.

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Différents environnements gravitationnels à 4 dimensions sont abordés dans ce thése : instantons gravitationnels et trous noirs aussi bien en relativité générale qu'en supergravité. La recherche de nouvelles solutions en relativité est un véritable défi. Cette tâche est nettement simplifiée dans l'hypothèse où l'on dispose d'un tenseur de Riemann auto-dual. Ces solutions sont dites instantons gravitationnels. L'évolution des instantons est décrite par un flot géométrique. Ce lien est analysé en détail, en focalisant l'attention sur le rôle du tensor de Ricci dans le flot géométrique. En espace de type Anti-de-Sitter (AdS), trouver de nouveaux trous noirs avec symétrie axiale est une question toujours ouverte. Cette question peut être posée dans le contexte des fluides holographiques. Trous noirs en rotation correspondent à des fluides aux vorticités particulières. En imposant que la solution soit régulière sur l'horizon, le fluide acquiert la forme d'un fluide parfait. Des conditions nécessaires afin que la correspondence entre solution gravitationnelle et théorie hydrodynamique, qui se fait usuellement par un développement perturbatif, puisse être ressommé et pour qu'on puisse trouver des solutions exactes de la relativité ont etées trouvées. Le comptage de l'entropie des trous noirs dans des espaces AdS ne fait toujours pas partie des résultats connus. Dans le cas des solutions en rotation des théories de supergravité N=2, une relation entre trous noirs extremaux non-BPS en espace plat et trous noirs BPS en espace AdS a été mise au point. La connexion entre cettes solutions donne des informations sur le comptage microscopique
The thesis is focused on the study of various gravitational environments in 4 dimensions: gravitational instantons and black holes both in general relativity and in supergravity. In general relativity, the search of new exact solutions is a challenging task. A peculiar simplifying assumption is the one of self-duality of the Riemann tensor. This condition provides a class of gravitational instantons. The temporal evolution of the instantons is described by a geometric flow. This connection has been analyzed in full details. In particular, the role of the Ricci tensor within the geometric flow bas been unraveled. It is a challenging question to exhibit new stationary axysymmetric black holes in AdS space. This question arises in the framework of holographic fluid dynamics. Rotating systems in the bulk correspond to fluids with non-trivial vorticity in the boundary. Regularity of the solution at the horizon implies that the boundary fluid has the form of a perfect-fluid. The holographic correspondence is usually done through a perturbative expansion. Necessary conditions have been found such that the expansion can be resummed and exact solutions of relativity can be generated. A microscopic counting of the entropy of black holes in AdS is not available yet. In the case of N=2 supergravity in four dimensions, a relation between rotating non-BPS extremal asymptotically flat black holes and BPS rotating asymptotically AdS black holes has been discovered. This procedure indicates that, for extremal black holes, a supersymmetric conformal field theory dual can be found, thus gaining insights on the role of gaugings in the microscopic counting
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Fedrow, Joseph Matthew. "Simulating Extreme Spacetimes on the Computer." Kyoto University, 2018. http://hdl.handle.net/2433/232238.

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Cole, Robert Harry. "Gravitational waves from extreme-mass-ratio inspirals." Thesis, University of Cambridge, 2015. https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.709066.

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Lima, William Couto Corrêa de. "Análogos de gravitação semi-clássica em física da matéria condensada." Universidade de São Paulo, 2008. http://www.teses.usp.br/teses/disponiveis/76/76131/tde-07042008-201206/.

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A presente dissertação tem como objeto de estudo sistemas da física da matéria condensada que sejam capazes de simular sistemas gravitacionais, tais como buracos negros e universos em expansão, onde processos quânticos tomam parte. Neste estudo nos debruçamos principalmente sobre o modelo do fluido e condensados de Bose-Einstein. No modelo do fluido exploramos a geometria efetiva que surge e os problemas de back-reaction e dos modos trans-planckianos de campos quânticos. No modelo baseado em condensados exploramos sua faceta cosmológica e a possibilidade de campos maciços. Além destes dois modelos de grande relevância na literatura, ainda expomos os análogos em cordas elásticas e os baseados em ondas na superfícies de fluidos e uma análise geral baseada no formalismo lagrangeano para campos.
This dissertation has as object of study systems of condensate-matter physics which can simulate gravitational systems like black holes and expanding universes where quantum processes take place. In this study we lay attention mainly on the fluid model and on Bose-Einstein-condensate-based models. In the fluid model we explore the features of the emergent geometry and other problems like the back-reaction and the trans-planckian modes of quantum fields. In the condensate-based models we explore their cosmological aspects and the possibility for massive fields. Moreover, we shall present two other models, the elastic string and the surface-wave-based models in fluids, and a very general analysis based on the Lagrangean formalism for fields.
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Books on the topic "Relativity and gravitational theory – General relativity – Black holes"

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Chow, Tai L. Gravity, black holes, and the very early universe: An introduction to general relativity and cosmology. New York: Springer, 2008.

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The formation of black holes in general relativity. Züich, Switzerland: European Mathematical Society, 2009.

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Berman, Marcelo Samuel. A primer in black holes, Mach's principle and gravitational energy. New York: Nova Science Publishers, 2008.

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Luminet, Jean-Pierre. Black holes. Cambridge [England]: Cambridge University Press, 1992.

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Ellwood, D. (David), 1966- editor of compilation, Rodnianski, Igor, 1972- editor of compilation, Staffilani, Gigliola, 1966- editor of compilation, and Wunsch, Jared, editor of compilation, eds. Evolution equations: Clay Mathematics Institute Summer School, evolution equations, Eidgenössische Technische Hochschule, Zürich, Switzerland, June 23-July 18, 2008. Providence, Rhode Island: American Mathematical Society, 2013.

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P, Minicozzi William, ed. A course in minimal surfaces. Providence, R.I: American Mathematical Society, 2011.

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Steane, Andrew M. Relativity Made Relatively Easy Volume 2. Oxford University Press, 2021. http://dx.doi.org/10.1093/oso/9780192895646.001.0001.

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This is a textbook on general relativity and cosmology for a physics undergraduate or an entry-level graduate course. General relativity is the main subject; cosmology is also discussed in considerable detail (enough for a complete introductory course). Part 1 introduces concepts and deals with weak-field applications such as gravitation around ordinary stars, gravimagnetic effects and low-amplitude gravitational waves. The theory is derived in detail and the physical meaning explained. Sources, energy and detection of gravitational radiation are discussed. Part 2 develops the mathematics of differential geometry, along with physical applications, and discusses the exact treatment of curvature and the field equations. The electromagnetic field and fluid flow are treated, as well as geodesics, redshift, and so on. Part 3 then shows how the field equation is solved in standard cases such as Schwarzschild-Droste, Reissner-Nordstrom, Kerr, and internal stellar structure. Orbits and related phenomena are obtained. Black holes are described in detail, including horizons, wormholes, Penrose process and Hawking radiation. Part 4 covers cosmology, first in terms of metric, then dynamics, structure formation and observational methods. The meaning of cosmic expansion is explained at length. Recombination and last scattering are calculated, and the quantitative analysis of the CMB is sketched. Inflation is introduced briefly but quantitatively. Part 5 is a brief introduction to classical field theory, including spinors and the Dirac equation, proceeding as far as the Einstein-Hilbert action. Throughout the book the emphasis is on making the mathematics as clear as possible, and keeping in touch with physical observations.
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Deruelle, Nathalie, and Jean-Philippe Uzan. Relativity in Modern Physics. Translated by Patricia de Forcrand-Millard. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198786399.001.0001.

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Newton’s ideas about how to represent space and time, his laws of dynamics, and his theory of gravitation established the conceptual foundation from which modern physics developed. This book offers a modern view of Newtonian theory, emphasizing those aspects needed for understanding quantum and relativistic contemporary physics. In 1905, Albert Einstein proposed a novel representation of space and time, special relativity. The text also presents relativistic dynamics in inertial and accelerated frames, as well as a detailed overview of Maxwell’s theory of electromagnetism, thus providing the background necessary for studying particle and accelerator physics, astrophysics, and Einstein’s theory of general relativity. In 1915, Einstein proposed a new theory of gravitation, general relativity. Finally, the text develops the geometrical framework in which Einstein’s equations are formulated and presents several key applications: black holes, gravitational radiation, and cosmology.
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d'Inverno, Ray, and James Vickers. Introducing Einstein's Relativity. 2nd ed. Oxford University PressOxford, 2022. http://dx.doi.org/10.1093/oso/9780198862024.001.0001.

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Abstract The aim of this book is to provide the reader with a sound mathematical introduction to Einstein’s theory of relativity, both special relativity and general relativity, as well as an understanding of the physical insights needed to explore the subject and the principles that guided Einstein in his search for the general theory of relativity. A feature of the book is that it has the numerous illustrative diagrams and exercises (of varying degrees of difficulty) which help the reader develop insight and confidence in using the mathematics. The book starts out by introducing special relativity and then the mathematics required for the rest of the book is carefully introduced. The principles underlying general relativity are introduced and it is shown how these lead to the basic field equations. These are then discussed and solved in some simple but physically important situations. The final three sections deal with the major applications of the theory and cover the topics of black holes, gravitational waves, and cosmology. These sections further develop the theory but also relate the theoretical predictions to current observations. These include the recent observation of gravitational waves by LIGO, evidence for supermassive black holes at the centre of most galaxies and the detailed observations of the cosmic microwave background that provide the evidence for modern cosmology.
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Cowen, Ron. Gravity's Century: From Einstein's Eclipse to Images of Black Holes. Harvard University Press, 2019.

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Book chapters on the topic "Relativity and gravitational theory – General relativity – Black holes"

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Adler, Ronald J. "Black Holes and Gravitational Collapse." In General Relativity and Cosmology, 141–58. Cham: Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-61574-1_10.

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Das, Anadijiban, and Andrew DeBenedictis. "Black Holes." In The General Theory of Relativity, 351–418. New York, NY: Springer New York, 2012. http://dx.doi.org/10.1007/978-1-4614-3658-4_5.

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Ferrari, Valeria, Leonardo Gualtieri, and Paolo Pani. "Gravitational waves from oscillating black holes." In General Relativity and its Applications, 299–320. Boca Raton: CRC Press, 2020.: CRC Press, 2020. http://dx.doi.org/10.1201/9780429491405-15.

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Mashhoon, Bahram. "Measurement Theory and General Relativity." In Black Holes: Theory and Observation, 269–84. Berlin, Heidelberg: Springer Berlin Heidelberg, 2003. http://dx.doi.org/10.1007/978-3-540-49535-2_13.

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Grøn, Øyvind. "Black Holes." In Lecture Notes on the General Theory of Relativity, 187–98. New York, NY: Springer New York, 2009. http://dx.doi.org/10.1007/978-0-387-88134-8_9.

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Prasanna, A. R., and Sai Iyer. "Kinematical Consequences of Inertial Forces in General Relativity." In Black Holes, Gravitational Radiation and the Universe, 189–206. Dordrecht: Springer Netherlands, 1999. http://dx.doi.org/10.1007/978-94-017-0934-7_12.

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Manton, Nicholas, and Nicholas Mee. "General Relativity." In The Physical World. Oxford University Press, 2017. http://dx.doi.org/10.1093/oso/9780198795933.003.0007.

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This chapter presents the physical motivation for general relativity, derives the Einstein field equation and gives concise derivations of the main results of the theory. It begins with the equivalence principle, tidal forces in Newtonian gravity and their connection to curved spacetime geometry. This leads to a derivation of the field equation. Tests of general relativity are considered: Mercury’s perihelion advance, gravitational redshift, the deflection of starlight and gravitational lenses. The exterior and interior Schwarzschild solutions are discussed. Eddington–Finkelstein coordinates are used to describe objects falling into non-rotating black holes. The Kerr metric is used to describe rotating black holes and their astrophysical consequences. Gravitational waves are described and used to explain the orbital decay of binary neutron stars. Their recent detection by LIGO and the beginning of a new era of gravitational wave astronomy is discussed. Finally, the gravitational field equations are derived from the Einstein–Hilbert action.
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Kolata, James J. "The General Theory of Relativity." In Neutron Stars, Black Holes and Gravitational Waves. IOP Publishing, 2019. http://dx.doi.org/10.1088/2053-2571/aafb08ch4.

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Steane, Andrew M. "Black holes." In Relativity Made Relatively Easy Volume 2, 274–300. Oxford University Press, 2021. http://dx.doi.org/10.1093/oso/9780192895646.003.0020.

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We discuss event horizons and black holes. First Birkhoff’s theorem is derived, and we consider the general nature of spherically symmetric spaces. Then the concepts of null surface, Killing horizon and event horizon are defined and related to one another. Cosmic censorship is briefly discussed. The Schwarzshild horizon is discussed in detail. The divergence or otherwise of redshift, acceleration, speed and proper time is obtained for infalling observers and for Schwarzschild observers. Eddington-Finkelstein coordinates are introduced and used to discuss gravitational collapse. The growth of the horizon is noted, and the causality structure is briefly considered via an introduction to the conformal (Penrose-Carter) diagram. The maximal extension is then presented, with the Kruskal-Szekeres coordinates and associated diagram. Wormholes are briefly discussed. The chapter finishes with a survey of astronomical evidence for black holes.
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Steane, Andrew M. "Gravitational waves." In Relativity Made Relatively Easy Volume 2, 65–92. Oxford University Press, 2021. http://dx.doi.org/10.1093/oso/9780192895646.003.0007.

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The theory of weak gravitational waves is discussed at length. The transverse traceless gauge is described, and the behaviour of plane wave solutions obtained. The impact of a wave on physical objects, and hence methods for their detection, are calculated. The laser interferometric gravitational wave detector is described. Sources such as binary stars are considered. The compact source approximation is employed, and the quadrupole formula relating the wave amplitude to the quadrupole of the source is obtained. Energy flux in gravitational waves is calculated by two methods, one more general, the other giving further physical insight. The total emitted power is obtained. These are lengthy calculations but they are presented in full. Finally they are applied in detail to a binary star with elliptical orbtis (the Hulse Taylor binary) and to a black hole merger detected by the LIGO interferometers.
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Conference papers on the topic "Relativity and gravitational theory – General relativity – Black holes"

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Ghezelbash, Masoud. "Gravitational perturbation in holography between rotating black holes and conformal field theory." In Proceedings of the MG15 Meeting on General Relativity. WORLD SCIENTIFIC, 2022. http://dx.doi.org/10.1142/9789811258251_0121.

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Ahn, Wha-Keun, Bogeun Gwak, Bum-Hoon Lee, and Wonwoo Lee. "Entropy preference of black holes in Dilatonic Einstein-Gauss-Bonnet theory of gravitation." In Proceedings of the MG14 Meeting on General Relativity. WORLD SCIENTIFIC, 2017. http://dx.doi.org/10.1142/9789813226609_0592.

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Stornaiolo, Cosimo. "The Cosmological Black Holes Hypothesis." In GENERAL RELATIVITY AND GRAVITATIONAL PHYSICS: 16th SIGRAV Conference on General Relativity and Gravitational Physics. AIP, 2005. http://dx.doi.org/10.1063/1.1891559.

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Visser, Matt. "Black holes in general relativity." In Black Holes in General Relativity and String Theory. Trieste, Italy: Sissa Medialab, 2009. http://dx.doi.org/10.22323/1.075.0001.

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LEMOS, JOSÉ P. S., and PAOLO PANI. "GRAVITATIONAL FIELDS WITH SOURCES, REGULAR BLACK HOLES, QUASIBLACK HOLES, AND ANALOGUE BLACK HOLES." In Proceedings of the MG13 Meeting on General Relativity. WORLD SCIENTIFIC, 2015. http://dx.doi.org/10.1142/9789814623995_0078.

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WHISKER, RICHARD. "GRAVITATIONAL LENSING BY BRANEWORLD BLACK HOLES." In Proceedings of the MG11 Meeting on General Relativity. World Scientific Publishing Company, 2008. http://dx.doi.org/10.1142/9789812834300_0232.

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Vanzo, L. "Asymptotics of Quasinormal Modes for Schwarzschild-de Sitter Black Holes." In GENERAL RELATIVITY AND GRAVITATIONAL PHYSICS: 16th SIGRAV Conference on General Relativity and Gravitational Physics. AIP, 2005. http://dx.doi.org/10.1063/1.1891550.

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GYULCHEV, GALIN N., and IVAN ZH STEFANOV. "STRONG GRAVITATIONAL LENSING BY PHANTOM BLACK HOLES." In Proceedings of the MG13 Meeting on General Relativity. WORLD SCIENTIFIC, 2015. http://dx.doi.org/10.1142/9789814623995_0365.

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BOZZA, VALERIO. "EXTREME GRAVITATIONAL LENSING BY SUPERMASSIVE BLACK HOLES." In Proceedings of the MG11 Meeting on General Relativity. World Scientific Publishing Company, 2008. http://dx.doi.org/10.1142/9789812834300_0086.

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MAJUMDAR, ARCHAN S., and NUPUR MUKHERJEE. "GRAVITATIONAL LENSING BY HIGHER DIMENSIONAL BLACK HOLES." In Proceedings of the MG11 Meeting on General Relativity. World Scientific Publishing Company, 2008. http://dx.doi.org/10.1142/9789812834300_0237.

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