Journal articles: 'Wave equations on black hole spacetimes'

1

Pailas, Theodoros. "“Time”-Covariant Schrödinger Equation and the Canonical Quantization of the Reissner–Nordström Black Hole." Quantum Reports 2, no. 3 (August 7, 2020): 414–41. http://dx.doi.org/10.3390/quantum2030029.

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A “time”-covariant Schrödinger equation is defined for the minisuperspace model of the Reissner–Nordström (RN) black hole, as a “hybrid” between the “intrinsic time” Schrödinger and Wheeler–DeWitt (WDW) equations. To do so, a reduced, regular, and “time(r)”-dependent Hamiltonian density was constructed, without “breaking” the re-parametrization covariance r→f(r˜). As a result, the evolution of states with respect to the parameter r and the probabilistic interpretation of the resulting quantum description is possible, while quantum schemes for different gauge choices are equivalent by construction. The solutions are found for Dirac’s delta and Gaussian initial states. A geometrical interpretation of the wavefunctions is presented via Bohm analysis. Alongside this, a criterion is presented to adjudicate which, between two singular spacetimes, is “more” or “less” singular. Two ways to adjudicate the existence of singularities are compared (vanishing of the probability density at the classical singularity and semi-classical spacetime singularity). Finally, an equivalence of the reduced equations with those of a 3D electromagnetic pp-wave spacetime is revealed.

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BINI, DONATO, CHRISTIAN CHERUBINI, ROBERT T. JANTZEN, and REMO RUFFINI. "DE RHAM WAVE EQUATION FOR TENSOR VALUED p-FORMS." International Journal of Modern Physics D 12, no. 08 (September 2003): 1363–84. http://dx.doi.org/10.1142/s0218271803003785.

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The de Rham Laplacian Δ (dR) for differential forms is a geometric generalization of the usual covariant Laplacian Δ, and it may be extended naturally to tensor-valued p-forms using the exterior covariant derivative associated with a metric connection. Using it the wave equation satisfied by the curvature tensors in general relativity takes its most compact form. This wave equation leads to the Teukolsky equations describing integral spin perturbations of black hole spacetimes.

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ATIQUR RAHMAN, M. "NUMERICAL SOLUTIONS OF IDEAL TWO-FLUID TRANSVERSE EQUATIONS VERY CLOSED TO THE EVENT HORIZON OF REISSNER–NORDSTRÖM–ANTI-DE SITTER BLACK HOLE." International Journal of Modern Physics D 22, no. 09 (June 26, 2013): 1350063. http://dx.doi.org/10.1142/s0218271813500636.

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The Alfvén and high frequency electromagnetic waves propagating in a relativistic two-fluid plasma influenced by the gravitational field of the Reissner–Nordström–anti-de Sitter (RNAdS) black hole have been investigated applying 3+1 split of spacetime. The extremal cases also discussed here based on the simple observation that the near-horizon geometry of a static extremal black hole contains two-dimensional anti-de Sitter factor even in the presence of positive cosmological constant. We reformulate the relativistic two-fluid equations with the set of simultaneous linear equations for the perturbations. We derive the dispersion relation for these waves and solve numerically for the wave number k.

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Momeni, Davood. "Covariant quantum-mechanical scattering via Stueckelberg–Horwitz–Piron theory." International Journal of Modern Physics D 29, no. 01 (January 2020): 2050008. http://dx.doi.org/10.1142/s021827182050008x.

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Based on the Stueckelberg–Horwitz–Piron theory of covariant quantum mechanics on curved spacetime, we solved the wave equations for a charged covariant harmonic oscillator in the background of a charged static spherically symmetric black hole. Using Green’s functions, we found an asymptotic form for the wave function in the lowest mode ([Formula: see text]-mode) and in higher moments. It has been proven that for [Formula: see text]-wave, in a definite range of solid angles, the differential cross-section depends effectively to on the magnetic and electric charges of the black hole.

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Al-Badawi, A., and I. sakalli. "Dirac and Klein–Gordon–Fock equations in Grumiller’s spacetime." International Journal of Geometric Methods in Modern Physics 15, no. 04 (March 13, 2018): 1850051. http://dx.doi.org/10.1142/s0219887818500512.

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We study the Dirac and the chargeless Klein–Gordon–Fock equations in the geometry of Grumiller’s spacetime that describes a model for gravity of a central object at large distances. The Dirac equation is separated into radial and angular equations by adopting the Newman–Penrose formalism. The angular part of the both wave equations are analytically solved. For the radial equations, we managed to reduce them to one dimensional Schrödinger-type wave equations with their corresponding effective potentials. Fermions’s potentials are numerically analyzed by serving their some characteristic plots. We also compute the quasinormal frequencies of the chargeless and massive scalar waves. With the aid of those quasinormal frequencies, Bekenstein’s area conjecture is tested for the Grumiller black hole. Thus, the effects of the Rindler acceleration on the waves of fermions and scalars are thoroughly analyzed.

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Rodríguez, J. F., J. A. Rueda, and R. Ruffini. "Strong-field gravitational-wave emission in Schwarzschild and Kerr geometries: some general considerations." EPJ Web of Conferences 168 (2018): 02006. http://dx.doi.org/10.1051/epjconf/201816802006.

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We have used the perturbations of the exact solutions of the Einstein equations to estimate the relativistic wave emission of a test particle orbiting around a black hole. We show how the hamiltonian equations of motion of a test particle augmented with the radiation-reaction force can establish a priori constraints on the possible phenomena occurring in the merger of compact objects. The dynamical evolution consists of a helicoidal sequence of quasi-circular orbits, induced by the radiation-reaction and the background spacetime. Near the innermost stable circular orbit the evolution is followed by a smooth transition and finally plunges geodesically into the black hole horizon. This analysis gives physical insight of the merger of two equal masses objects.

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Allahyari, Alireza, Javad T. Firouzjaee, and Reza Mansouri. "Gravitational collapse in the AdS background and the black hole formation." International Journal of Modern Physics D 25, no. 01 (January 2016): 1650005. http://dx.doi.org/10.1142/s021827181650005x.

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We study the time evolution of the Misner-Sharp mass and the apparent horizon for gravitational collapse of a massless scalar field in the [Formula: see text] spacetime for both cases of narrow and broad waves by numerically solving the Einstein’s equations coupled to a massless scalar field. This is done by relying on the full dynamics of the collapse including the concept of the dynamical horizon. It turns out that the Misner-Sharp mass is everywhere constant except for a rapid change across a thin shell defined by the density profile of the collapsing wave. By studying the evolution of the apparent horizon, indicating the formation of a black hole at different times we see how asymptotically an event horizon forms. The dependence of the thermalization time on the radius of the initial black hole event horizon is also studied.

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Bokhari, Ashfaque H., A. H. Kara, B. B. I. Gadjagboui, and Ghulam Shabbir. "Symmetries and conservation laws of some asymptotically symmetric spacetimes of interest in gravitational waves." International Journal of Geometric Methods in Modern Physics 16, no. 10 (October 2019): 1950152. http://dx.doi.org/10.1142/s0219887819501524.

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In this paper, we discuss symmetries and the corresponding conservation laws of certain exact solutions of the Einstein field equations (EFEs) representing a Schwarzschild black hole and gravitational waves in asymptotically flat space times. Of particular interest are symmetries of asymptotically flat spacetimes because they admit a property that identifies them for the existence of gravitational waves there. In the light of this fact, we discuss symmetry algebras of a few recently published solutions of Einstein equations in asymptotically flat metrics. Given the fact that gravitational waves are of great interest in relativity, we focus in this paper on finding the type of symmetries they admit and their corresponding conservation laws. We also show how these symmetries are radically different from the other well-known symmetries and present necessary condition that distinguishes them.

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Tokgöz, Gülni̇hal, and İzzet Sakallı. "Fermion clouds around z = 0 Lifshitz black holes." International Journal of Geometric Methods in Modern Physics 17, no. 09 (August 2020): 2050143. http://dx.doi.org/10.1142/s0219887820501431.

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In this work, the Dirac equation is studied in the [Formula: see text] Lifshitz black hole ([Formula: see text]LBH) spacetime. The set of equations representing the Dirac equation in the Newman–Penrose (NP) formalism is decoupled into a radial set and an angular set. The separation constant is obtained with the aid of the spin weighted spheroidal harmonics. The radial set of equations, which are independent of mass, is reduced to Zerilli equations (ZEs) with their associated potentials. In the near horizon (NH) region, these equations are solved in terms of the Bessel functions of the first and second kinds arising from the fermionic perturbation on the background geometry. For computing the boxed quasinormal modes (BQNMs) instead of the ordinary quasinormal modes (QNMs), we first impose the purely ingoing wave condition at the event horizon. Then, Dirichlet boundary condition (DBC) and Newmann boundary condition (NBC) are applied in order to get the resonance conditions. For solving the resonance conditions, we follow the Hod’s iteration method. Finally, Maggiore’s method (MM) is employed to derive the entropy/area spectra of the [Formula: see text]LBH which are shown to be equidistant.

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Most, Elias R., L. Jens Papenfort, Samuel D. Tootle, and Luciano Rezzolla. "On accretion discs formed in MHD simulations of black hole–neutron star mergers with accurate microphysics." Monthly Notices of the Royal Astronomical Society 506, no. 3 (July 1, 2021): 3511–26. http://dx.doi.org/10.1093/mnras/stab1824.

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ABSTRACT Remnant accretion discs formed in compact object mergers are an important ingredient in the understanding of electromagnetic afterglows of multimessenger gravitational-wave events. Due to magnetically and neutrino-driven winds, a significant fraction of the disc mass will eventually become unbound and undergo r-process nucleosynthesis. While this process has been studied in some detail, previous studies have typically used approximate initial conditions for the accretion discs, or started from purely hydrodynamical simulations. In this work, we analyse the properties of accretion discs formed from near equal-mass black hole–neutron star mergers simulated in general-relativistic magnetohydrodynamics in dynamical spacetimes with an accurate microphysical description. The post-merger systems were evolved until $120\, {\rm ms}$ for different finite-temperature equations of state and black hole spins. We present a detailed analysis of the fluid properties and of the magnetic-field topology. In particular, we provide analytic fits of the magnetic-field strength and specific entropy as a function of the rest-mass density, which can be used for the construction of equilibrium disc models. Finally, we evolve one of the systems for a total of $350\, \rm ms$ after merger and study the prospect for eventual jet launching. While our simulations do not reach this stage, we find clear evidence of continued funnel magnetization and clearing, a prerequisite for any jet-launching mechanism.

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11

Moreno, Claudia, Juan Carlos Degollado, Darío Núñez, and Carlos Rodríguez-Leal. "Gravitational and Electromagnetic Perturbations of a Charged Black Hole in a General Gauge Condition." Particles 4, no. 2 (March 25, 2021): 106–28. http://dx.doi.org/10.3390/particles4020012.

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We derive a set of coupled equations for the gravitational and electromagnetic perturbation in the Reissner–Nordström geometry using the Newman–Penrose formalism. We show that the information of the physical gravitational signal is contained in the Weyl scalar function Ψ4, as is well known, but for the electromagnetic signal, the information is encoded in the function χ, which relates the perturbations of the radiative Maxwell scalars φ2 and the Weyl scalar Ψ3. In deriving the perturbation equations, we do not impose any gauge condition and as a limiting case, our analysis contains previously obtained results, for instance, those from Chandrashekhar’s book. In our analysis, we also include the sources for the perturbations and focus on a dust-like charged fluid distribution falling radially into the black hole. Finally, by writing the functions on the basis of spin-weighted spherical harmonics and the Reissner–Nordström spacetime in Kerr–Schild type coordinates, a hyperbolic system of coupled partial differential equations is presented and numerically solved. In this way, we completely solve a system that generates a gravitational signal as well as an electromagnetic/gravitational one, which sets the basis to find correlations between them and thus facilitates gravitational wave detection via electromagnetic signals.

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SARBACH, OLIVIER, and MANUEL TIGLIO. "BOUNDARY CONDITIONS FOR EINSTEIN'S FIELD EQUATIONS: MATHEMATICAL AND NUMERICAL ANALYSIS." Journal of Hyperbolic Differential Equations 02, no. 04 (December 2005): 839–83. http://dx.doi.org/10.1142/s0219891605000634.

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Outer boundary conditions for strongly and symmetric hyperbolic formulations of 3D Einstein's field equations with a live gauge condition are discussed. The boundary conditions have the property that they ensure constraint propagation and control in a sense made precise in this article the physical degrees of freedom at the boundary. We use Fourier–Laplace transformation techniques to find necessary conditions for the well posedness of the resulting initial-boundary value problem and integrate the resulting three-dimensional nonlinear equations using a finite-differencing code. We obtain a set of constraint-preserving boundary conditions which pass a robust numerical stability test. We explicitly compare these new boundary conditions to standard, maximally dissipative ones through Brill wave evolutions. Our numerical results explicitly show that in the latter case the constraint variables, describing the violation of the constraints, do not converge to zero when resolution is increased while for the new boundary conditions, the constraint variables do decrease as resolution is increased. As an application, we inject pulses of "gravitational radiation" through the boundaries of an initially flat spacetime domain, with enough amplitude to generate strong fields and induce large curvature scalars, showing that our boundary conditions are robust enough to handle nonlinear dynamics. We expect our boundary conditions to be useful for improving the accuracy and stability of current binary black hole and binary neutron star simulations, for a successful implementation of characteristic or perturbative matching techniques, and other applications. We also discuss limitations of our approach and possible future directions.

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Arslanaliev, Adam M., and Alexei J. Nurmagambetov. "Scattering on Quasi-Spherical Black-Holes: Features and Beyond." Physics 3, no. 1 (January 28, 2021): 17–41. http://dx.doi.org/10.3390/physics3010004.

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Recent developments in the gravitational waves interferometry require more pertinent theoretical models of gravitational waves generation and propagation. Untouched possible mechanisms of spin-2 spacetime perturbations production, we will consider their subsequent scattering on other black holes (BHs). Specifically, we consider a generalization of the Regge-Wheeler-Zerilli equations for the case of distorted BHs (BHs surrounded with matter) in Minkowski and Anti-de Sitter spacetimes, the metric potential of which obeys the Liouville equation. We establish significant differences in scattering characteristics of waves of different spins and angular momenta, including the gravitational waves, caused by losing the spherical symmetry of their propagation background. In particular, we demonstrate the strong impact of the background geometry deformation on the grey-body factors, hence on the absorption cross-sections of scattering waves, and explore the issue of stability of the background geometry upon changing the deformation degree parameters.

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Nambu, Yasusada, and Sousuke Noda. "Wave optics in black hole spacetimes: the Schwarzschild case." Classical and Quantum Gravity 33, no. 7 (March 9, 2016): 075011. http://dx.doi.org/10.1088/0264-9381/33/7/075011.

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MYUNG, Y. S., and H. W. LEE. "UNITARITY ISSUE IN BTZ BLACK HOLES." Modern Physics Letters A 21, no. 22 (July 20, 2006): 1737–48. http://dx.doi.org/10.1142/s0217732306021050.

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We study the wave equation for a massive scalar in three-dimensional AdS-black hole spacetimes to understand the unitarity issues in a semiclassical way. Here we introduce four interesting spacetimes: the non-rotating BTZ black hole (NBTZ), pure AdS spacetime (PADS), massless BTZ black hole (MBTZ), and extremal BTZ black hole (EBTZ). Our method is based on the potential analysis and solving the wave equation to find the condition for the frequency ω exactly. In the NBTZ case, one finds the quasinormal (complex and discrete) modes which signals for a non-unitary evolution. Real and discrete modes are found for the PADS case, which means that it is unitary obviously. On the other hand, we find real and continuous modes for the two extremal black holes of MBTZ and EBTZ. It suggests that these could be candidates for the unitary system.

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JARAMILLO, JOSÉ LUIS. "AN INTRODUCTION TO LOCAL BLACK HOLE HORIZONS IN THE 3+1 APPROACH TO GENERAL RELATIVITY." International Journal of Modern Physics D 20, no. 11 (October 19, 2011): 2169–204. http://dx.doi.org/10.1142/s0218271811020366.

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We present an introduction to dynamical trapping horizons as quasi-local models for black hole horizons, from the perspective of an Initial Value Problem approach to the construction of generic black hole spacetimes. We focus on the geometric and structural properties of these horizons aiming, as a main application, at the numerical evolution and analysis of black hole spacetimes in astrophysical scenarios. In this setting, we discuss their dual role as an a priori ingredient in certain formulations of Einstein equations and as an a posteriori tool for the diagnosis of dynamical black hole spacetimes. Complementary to the first-principles discussion of quasi-local horizon physics, we place an emphasis on the rigidity properties of these hypersurfaces and their role as privileged geometric probes into near-horizon strong-field spacetime dynamics.

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JARAMILLO, JOSÉ LUIS. "AN INTRODUCTION TO LOCAL BLACK HOLE HORIZONS IN THE 3+1 APPROACH TO GENERAL RELATIVITY." International Journal of Modern Physics: Conference Series 07 (January 2012): 31–66. http://dx.doi.org/10.1142/s2010194512004175.

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We present an introduction to dynamical trapping horizons as quasi-local models for black hole horizons, from the perspective of an Initial Value Problem approach to the construction of generic black hole spacetimes. We focus on the geometric and structural properties of these horizons aiming, as a main application, at the numerical evolution and analysis of black hole spacetimes in astrophysical scenarios. In this setting, we discuss their dual role as an a priori ingredient in certain formulations of Einstein equations and as an a posteriori tool for the diagnosis of dynamical black hole spacetimes. Complementary to the first-principles discussion of quasi-local horizon physics, we place an emphasis on the rigidity properties of these hypersurfaces and their role as privileged geometric probes into near-horizon strong-field spacetime dynamics.

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Anninos, Peter, David Bemstein, Steve Brandt, David Hobill, Ed Seidel, and Larry Smarr. "Oscillating Apparent Horizons in Numerically Generated Spacetimes." Australian Journal of Physics 48, no. 6 (1995): 1027. http://dx.doi.org/10.1071/ph951027.

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We investigate the evolution of the apparent horizon in three families of numerically generated spacetimes: the 'black hole plus Brill wave' spacetimes of Bernstein et al., the non-time symmetric generalisation of this by Brandt, and the Misner two black hole spacetime. Various measures of the curvature and shape of the horizon are shown as a function of coordinate time at infinity and it is found that the horizon oscillates at the lowest quasinormal mode frequency of the hole. In addition, in the spacetimes with angular momentum the total angular momentum of the final hole can be read off from the oscillations of the horizon directly without having to extract it from the gravitational radiation emitted by the hole.

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Gundlach, Carsten, and Paul Walker. "Causal differencing of flux-conservative equations applied to black hole spacetimes." Classical and Quantum Gravity 16, no. 3 (January 1, 1999): 991–1010. http://dx.doi.org/10.1088/0264-9381/16/3/026.

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Mena, Filipe C. "Spacetime Junctions and the Collapse to Black Holes in Higher Dimensions." Advances in Mathematical Physics 2012 (2012): 1–14. http://dx.doi.org/10.1155/2012/638726.

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We review recent results about the modelling of gravitational collapse to black holes in higher dimensions. The models are constructed through the junction of two exact solutions of the Einstein field equations: an interior collapsing fluid solution and a vacuum exterior solution. The vacuum exterior solutions are either static or containing gravitational waves. We then review the global geometrical properties of the matched solutions which, besides black holes, may include the existence of naked singularities and wormholes. In the case of radiating exteriors, we show that the data at the boundary can be chosen to be, in some sense, arbitrarily close to the data for the Schwarzschild-Tangherlini solution.

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Araneda, Bernardo. "Symmetry operators and decoupled equations for linear fields on black hole spacetimes." Classical and Quantum Gravity 34, no. 3 (December 29, 2016): 035002. http://dx.doi.org/10.1088/1361-6382/aa51ff.

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Li, Jin, Kai Lin, Hao Wen, and Wei-Liang Qian. "Gravitational Quasinormal Modes of Regular Phantom Black Hole." Advances in High Energy Physics 2017 (2017): 1–19. http://dx.doi.org/10.1155/2017/5234214.

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We investigate the gravitational quasinormal modes (QNMs) for a type of regular black hole (BH) known as phantom BH, which is a static self-gravitating solution of a minimally coupled phantom scalar field with a potential. The studies are carried out for three different spacetimes: asymptotically flat, de Sitter (dS), and anti-de Sitter (AdS). In order to consider the standard odd parity and even parity of gravitational perturbations, the corresponding master equations are derived. The QNMs are discussed by evaluating the temporal evolution of the perturbation field which, in turn, provides direct information on the stability of BH spacetime. It is found that in asymptotically flat, dS, and AdS spacetimes the gravitational perturbations have similar characteristics for both odd and even parities. The decay rate of perturbation is strongly dependent on the scale parameterb, which measures the coupling strength between phantom scalar field and the gravity. Furthermore, through the analysis of Hawking radiation, it is shown that the thermodynamics of such regular phantom BH is also influenced byb. The obtained results might shed some light on the quantum interpretation of QNM perturbation.

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DOTTI, GUSTAVO, REINALDO J. GLEISER, and IGNACIO F. RANEA-SANDOVAL. "INSTABILITIES IN KERR SPACETIMES." International Journal of Modern Physics E 20, supp01 (December 2011): 27–31. http://dx.doi.org/10.1142/s0218301311040049.

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We present a generalization of previous results regarding the stability under gravitational perturbations of nakedly singular super extreme Kerr spacetime and Kerr black hole interior beyond the Cauchy horizon. To do so we study solutions to the radial and angular Teukolsky's equations with different spin weights, particulary s = ±1 representing electromagnetic perturbations, s = ±1/2 representing a perturbation by a Dirac field and s = 0 representing perturbations by a scalar field. By analizing the properties of radial and angular eigenvalues we prove the existence of an infinite family of unstable modes.

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Aydın, Hüseyi̇n, and Meli̇s Ulu Dog̃ru. "Cylindrically symmetric unimodular f(R) black holes." International Journal of Geometric Methods in Modern Physics 18, no. 07 (March 11, 2021): 2150101. http://dx.doi.org/10.1142/s0219887821501012.

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In this paper, we examine massless scalar field by using unimodular [Formula: see text] theory. It is taken into account unimodular and cylindrically symmetric spacetime which provides convenience in researching black hole. The field equations in unimodular [Formula: see text] theory for given spacetime with massless scalar field and additional Bianchi identities are solved. Cylindrically symmetric anti-de Sitter (AdS)–Schwarzschild-like and AdS–Reissner–Nordström-like black hole spacetimes are achieved. Equations of motion are derived by using Hamiltonian. Orbits of massless test particles are depicted. Obtained line element asymptotically converges to dS/AdS spacetime. Weak and strong energy conditions of the massless scalar field are obtained with Raychaudhuri equations in unimodular [Formula: see text] theory. Also, stiff fluid interpretation of scalar field is reviewed.

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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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Nashed, G. G. L. "Rotating charged black hole spacetimes in quadratic f(R) gravitational theories." International Journal of Modern Physics D 27, no. 07 (May 2018): 1850074. http://dx.doi.org/10.1142/s0218271818500748.

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Motivated by the substantial modifications of gravitational theories and by the models that come out of [Formula: see text], we apply the field equation of the charged [Formula: see text] as well as a general vector potential containing three unknown functions to two spherically symmetric spacetimes. We solve the output of the differential equations and derive a class of black holes that are electrically and magnetically rotating spacetimes. The asymptotic behavior of these black holes acts as anti-de Sitter spacetime. Moreover, these solutions have asymptotic curvature singularities as those of General Relativity. We investigate this by calculating the invariants of curvature. Also, we address the issue of the energy conditions and show that the strong energy condition is satisfied provided [Formula: see text]. Finally, we compute the conserved quantities like mass and angular momentum.

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Stuchlík, Zdeněk, and Jan Schee. "Circular geodesic of Bardeen and Ayon–Beato–Garcia regular black-hole and no-horizon spacetimes." International Journal of Modern Physics D 24, no. 02 (February 2015): 1550020. http://dx.doi.org/10.1142/s0218271815500200.

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In this paper, we study circular geodesic motion of test particles and photons in the Bardeen and Ayon–Beato–Garcia (ABG) geometry describing spherically symmetric regular black-hole or no-horizon spacetimes. While the Bardeen geometry is not exact solution of Einstein's equations, the ABG spacetime is related to self-gravitating charged sources governed by Einstein's gravity and nonlinear electrodynamics. They both are characterized by the mass parameter m and the charge parameter g. We demonstrate that in similarity to the Reissner–Nordstrom (RN) naked singularity spacetimes an antigravity static sphere should exist in all the no-horizon Bardeen and ABG solutions that can be surrounded by a Keplerian accretion disc. However, contrary to the RN naked singularity spacetimes, the ABG no-horizon spacetimes with parameter g/m > 2 can contain also an additional inner Keplerian disc hidden under the static antigravity sphere. Properties of the geodesic structure are reflected by simple observationally relevant optical phenomena. We give silhouette of the regular black-hole and no-horizon spacetimes, and profiled spectral lines generated by Keplerian rings radiating at a fixed frequency and located in strong gravity region at or nearby the marginally stable circular geodesics. We demonstrate that the profiled spectral lines related to the regular black-holes are qualitatively similar to those of the Schwarzschild black-holes, giving only small quantitative differences. On the other hand, the regular no-horizon spacetimes give clear qualitative signatures of their presence while compared to the Schwarschild spacetimes. Moreover, it is possible to distinguish the Bardeen and ABG no-horizon spacetimes, if the inclination angle to the observer is known.

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DE OLIVEIRA, H. P., and E. L. RODRIGUES. "BLACK HOLES COLLISION IN GENERAL ROBINSON-TRAUTMAN SPACETIMES: WAVE FORMS AND THE EFFICIENCY OF THE GRAVITATIONAL WAVE EXTRACTION." International Journal of Modern Physics: Conference Series 03 (January 2011): 408–16. http://dx.doi.org/10.1142/s2010194511000924.

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We analyze the non-frontal collisions of two Schwarzschild black holes in the realm of general Robinson-Trautman spacetimes using a numerical code based on spectral methods. In this process, two black holes collide and form a single black hole while a certain amount of the initial mass is carried away by gravitational waves. We determined the forms of the gravitational waves and the efficiency of this process for frontal and non-frontal collisions. We found numerical evidence that the distribution of mass qloss can be described by a function typically used in nonextensive statistics.

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Liao, Hao, Ju-Hua Chen, Ping Liao, and Yong-Jiu Wang. "Absorption/Scattering of Massless Dirac Wave from Black Hole Spacetimes with Cosmic String." Communications in Theoretical Physics 62, no. 2 (August 2014): 227–34. http://dx.doi.org/10.1088/0253-6102/62/2/10.

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Couch, W. E. "Solutions to wave equations on black hole geometries. II." Journal of Mathematical Physics 26, no. 9 (September 1985): 2286–96. http://dx.doi.org/10.1063/1.526811.

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Dariescu, Marina-Aura, Ciprian Dariescu, and Cristian Stelea. "Massless fermions on static general prolate metrics and their Heun solutions." Modern Physics Letters A 35, no. 07 (November 27, 2019): 2050036. http://dx.doi.org/10.1142/s0217732320500364.

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Employing a pseudo-orthonormal coordinate-free approach, we write down the Dirac equation in spacetimes with static general prolate metrics. As examples, we consider the electrically charged C-metric, the vacuum C-metric, the Reissner–Nordström and Schwarzschild spacetimes and the BBMB black hole and show that the solutions to the Dirac equations for particles in these spacetimes can be derived in terms of Heun’s general functions and their confluent and double confluent forms. By imposing boundary conditions to the radial solutions, the so-called resonant frequencies are obtained.

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HUBENY, VERONIKA E., and MUKUND RANGAMANI. "HORIZONS AND PLANE WAVES: A REVIEW." Modern Physics Letters A 18, no. 38 (December 14, 2003): 2699–711. http://dx.doi.org/10.1142/s0217732303012428.

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We review the attempts to construct black hole/string solutions in asymptotically plane wave spacetimes. First, we demonstrate that geometries admitting a covariantly constant null Killing vector cannot admit event horizons, which implies that pp-waves cannot describe black holes. However, relaxing the symmetry requirements allows us to generate solutions which do possess regular event horizons while retaining the requisite asymptotic properties. In particular, we present two solution generating techniques and use them to construct asymptotically plane wave black string/brane geometries.

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Gajic, Dejan, and Claude Warnick. "Quasinormal Modes in Extremal Reissner–Nordström Spacetimes." Communications in Mathematical Physics 385, no. 3 (June 27, 2021): 1395–498. http://dx.doi.org/10.1007/s00220-021-04137-4.

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AbstractWe present a new framework for characterizing quasinormal modes (QNMs) or resonant states for the wave equation on asymptotically flat spacetimes, applied to the setting of extremal Reissner–Nordström black holes. We show that QNMs can be interpreted as honest eigenfunctions of generators of time translations acting on Hilbert spaces of initial data, corresponding to a suitable time slicing. The main difficulty that is present in the asymptotically flat setting, but is absent in the previously studied asymptotically de Sitter or anti de Sitter sub-extremal black hole spacetimes, is that $$L^2$$ L 2 -based Sobolev spaces are not suitable Hilbert space choices. Instead, we consider Hilbert spaces of functions that are additionally Gevrey regular at infinity and at the event horizon. We introduce $$L^2$$ L 2 -based Gevrey estimates for the wave equation that are intimately connected to the existence of conserved quantities along null infinity and the event horizon. We relate this new framework to the traditional interpretation of quasinormal frequencies as poles of the meromorphic continuation of a resolvent operator and obtain new quantitative results in this setting.

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FERRARI, V., L. GUALTIERI, and F. PANNARALE. "BLACK HOLE–NEUTRON STAR COALESCING BINARIES." International Journal of Modern Physics D 19, no. 08n10 (August 2010): 1241–48. http://dx.doi.org/10.1142/s0218271810017871.

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Coalescing black hole–neutron star binaries have been invoked as possible progenitors of short gamma-ray bursts and are also among the most promising gravitational wave sources to be detected by ground-based laser interferometers. When the star is disrupted by tidal interactions before reaching the innermost stable circular orbit, the gravitational wave signal emitted by the system is expected to exhibit a cutoff frequency which is a distinctive feature of the waveform. We evaluate this frequency for several equations of state, describing the matter inside the neutron star, and combinations of the binary parameters. We show that, if this frequency will be found in a detected gravitational wave, it will provide valuable information on the behavior of matter in the stellar core.

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Lin, Hai, K. Saifullah, and Shing-Tung Yau. "Accelerating black holes, spin-$\frac32$ fields and C-metric." Modern Physics Letters A 30, no. 08 (March 4, 2015): 1550044. http://dx.doi.org/10.1142/s0217732315500443.

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We consider spin-[Formula: see text] particles on the background of general accelerating black holes and the C-metric. The Rarita–Schwinger equations of spin-[Formula: see text] particles are analyzed on these backgrounds. The emission and absorption probabilities of these particles on these spacetimes are calculated. These backgrounds which we analyze contain both black hole horizon and acceleration horizon, and have general electric and magnetic charges, rotation, and acceleration parameter. Other physical quantities of the spin-[Formula: see text] field near the acceleration horizon are also computed.

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Perjés, Zoltán. "Letter: Wave Equations for the Perturbations of a Charged Black Hole." General Relativity and Gravitation 35, no. 7 (July 2003): 1291–97. http://dx.doi.org/10.1023/a:1024410110825.

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PADMANABHAN, T. "THERMODYNAMICS OF HORIZONS: A COMPARISON OF SCHWARZSCHILD, RINDLER AND de SITTER SPACETIMES." Modern Physics Letters A 17, no. 15n17 (June 7, 2002): 923–42. http://dx.doi.org/10.1142/s021773230200751x.

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The notions of temperature, entropy and 'evaporation', usually associated with spacetimes with horizons, are analyzed using general approach and the following results, applicable to different spacetimes, are obtained at one go. (i) The concept of temperature associated with the horizon is derived in a unified manner and is shown to arise from purely kinematic considerations. (ii) QFT near any horizon is mapped to a conformal field theory without introducing concepts from string theory. (iii) For spherically symmetric spacetimes (in D = 1 + 3) with a horizon at r = l, the partition function has the generic form Z ∝ exp [S - βE], where S = (1/4)4πl2 and |E| = (l/2). This analysis reproduces the conventional result for the black hole spacetimes and provides a simple and consistent interpretation of entropy and energy E = - (1/2)H-1 for deSitter spacetime. The classical Einstein's equations for this spacetime can be expressed as a thermodynamic identity, TdS - dE = PdV with the same variables. (iv) For the Rindler spacetime the entropy per unit transverse area turns out to be (1/4) while the energy is zero. (v) In the case of a Schwarzschild black hole there exist quantum states (like Unruh vacuum) which are not invariant under time reversal and can describe black hole evaporation. There also exist quantum states (like Hartle-Hawking vacuum) in which temperature is well-defined but there is no flow of radiation to infinity. In the case of deSitter universe or Rindler patch in flat spacetime, one usually uses quantum states analogous to Hartle-Hawking vacuum and obtains a temperature without the corresponding notion of evaporation. It is, however, possible to construct the analogues of Unruh vacuum state in the other cases as well. The implications are briefly discussed.

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CAI, RONG-GEN, and YUAN-ZHONG ZHANG. "ENTROPY OF SCALAR FIELDS IN REISSNER–NORDSTRÖM–(ANTI-)DE SITTER SPACETIMES." Modern Physics Letters A 11, no. 25 (August 20, 1996): 2027–36. http://dx.doi.org/10.1142/s0217732396002010.

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The entropy of a free scalar field is calculated in the Reissner–Nordström–(anti-)de Sitter spacetimes. Due to the presence of the cosmological horizon in the Reissner–Nordström–de Sitter spacetime, we introduce a cutoff at the cosmological horizon, besides the cutoff at the horizon of black holes in the brick wall model. The entropy is found to be the sum of two terms, which are proportional to the area of the cosmological horizon and of black hole horizon, respectively. In the Reissner–Nordström–anti-de Sitter spacetime the contribution of the anti-de Sitter background to the entropy of scalar fields vanishes when an infinite volume is taken. The entropy of scalar fields is also evaluated in some special backgrounds described by solutions of Einstein–Maxwell equations with a cosmological constant, such as the cold black holes, lukewarm black holes, ultracold solutions, a naked singularity in de Sitter space, and the de Sitter space. The physical meaning of some results is briefly discussed.

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ARANHA, R. F., I. DAMIÃO SOARES, H. P. OLIVEIRA, and E. V. TONINI. "ENERGY AND MOMENTUM LOSS BY GRAVITATIONAL RADIATION EMISSION IN THE COLLISION OF TWO SCHWARZSCHILD BLACK HOLES." International Journal of Modern Physics A 24, no. 08n09 (April 10, 2009): 1583–87. http://dx.doi.org/10.1142/s0217751x09045042.

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We analyze the head-on collision of two boosted Schwarzschild black holes and the mass-energy loss of the system by gravitational wave emission, in the realm of Robinson-Trautman (RT) spacetimes. The characteristic initial data for the problem are constructed, and evolved by RT equation integrated by numerical codes based on the Galerkin method. The emission of gravitational waves is typical bremsstrahlung at early times and the final configuration is that of a boosted black hole with larger (Bondi) rest mass and smaller velocity parameter. The efficiency Δ of the process of energy extraction by gravitational radiation is evaluated and satisfies a nonextensive distribution with entropic index q ≃ 1/2. The final momentum of the remnant black hole has a maximum which depends on the ratio of the masses of the initial black holes.

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SLANÝ, PETR, JIŘÍ KOVÁŘ, and ZDENĚK STUCHLÍK. "RELATIVISTIC DYNAMICS WITH COSMOLOGICAL CONSTANT: CIRCULAR GEODESIC MOTION OF TEST PARTICLES." International Journal of Modern Physics A 24, no. 08n09 (April 10, 2009): 1598–601. http://dx.doi.org/10.1142/s0217751x09045078.

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We present results of our recent studies concerning effects of Λ > 0 in astrophysically motivated problems. Here we summarize properties of circular geodesic motion of test particles in the equatorial plane of Kerr-de Sitter black-hole and naked-singularity spacetimes. Along with the standard analysis of geodesic equations of the ordinary geometry, we introduce alternative inertial forces formalism defined within the General Theory of Relativity in the framework of optical reference geometry.

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Bokulić, Ana, and Ivica Smolić. "Immersing the Schwarzschild Black Hole in Test Nonlinear Electromagnetic Fields." Physical Sciences Forum 2, no. 1 (February 22, 2021): 22. http://dx.doi.org/10.3390/ecu2021-09301.

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Killing vector fields can be used as gauge vector potentials since the associated electromagnetic field tensor automatically satisfies the source-free Maxwell’s equations in vacuum spacetimes. This fact enabled Wald to find the form of the electromagnetic tensor corresponding to the Kerr black hole immersed in a uniform test magnetic field. We present the generalisation of this result, which is valid for static black holes surrounded by nonlinear electromagnetic fields. The first obstacle we encountered when dealing with the nonlinear electrodynamics was that the above-described ansatz no longer works. Secondly, finding the exact solution in a closed form proved to be a rather challenging task because it would require solving a highly nonlinear differential equation. The alternative approach is via perturbative expansion around the original Wald’s solution. We obtain the equation which determines the lowest order correction to the gauge vector field 1-form and magnetic scalar potential. With the main focus on the Born–Infeld and Euler–Heisenberg theories on the Schwarzschild background, we calculate the aforementioned correction. Additionally, we show that this perturbative correction does not change electric and magnetic Komar charges or the asymptotic behaviour of the field. Finally, stating physical arguments, we justify the usage of the perturbative approach.

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Barreto, W., H. P. de Oliveira, and E. L. Rodrigues. "Nonlinear interaction between electromagnetic and gravitational waves: An appraisal." International Journal of Modern Physics D 26, no. 12 (October 2017): 1743017. http://dx.doi.org/10.1142/s0218271817430179.

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Wave propagation of field disturbances is ubiquitous. The electromagnetic and gravitational are cousin theories in which the corresponding waves play a relevant role to understand several related physical aspects. It has been established that small electromagnetic waves can generate gravitational waves and vice versa when scattered by a charged black hole. In the realm of cylindrical spacetimes, we present here a simple nonlinear effect of the conversion of electromagnetic to gravitational waves reflected by the amount of mass extracted from them.

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Degollado, Juan Carlos. "Electromagnetic and gravitational signatures of accretion into black holes." International Journal of Modern Physics D 24, no. 09 (July 31, 2015): 1542004. http://dx.doi.org/10.1142/s0218271815420043.

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In this paper, the gravitational and electromagnetic signals due to accretion of charged fluids into a Schwarzschild black hole is revisited. We set up the perturbed Einstein equations and Maxwell equations coupled to the fluid equations on a stationary black hole as a system of differential equations that can be integrated as an initial value problem. We numerically investigate cases in which we varied the properties of the fluid. Our scenario may provide an electromagnetic counterpart to gravitational waves in many situations of interest, enabling easier extraction and verification of gravitational waveforms from gravitational wave detection. We find that the features of the resulting electromagnetic signals depend on the properties and dynamics of the flow.

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Bizoń, Piotr, and Helmut Friedrich. "A remark about wave equations on the extreme Reissner–Nordström black hole exterior." Classical and Quantum Gravity 30, no. 6 (February 18, 2013): 065001. http://dx.doi.org/10.1088/0264-9381/30/6/065001.

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Pfeifer, Christian, and Sebastian Schuster. "Static Spherically Symmetric Black Holes in Weak f(T)-Gravity." Universe 7, no. 5 (May 17, 2021): 153. http://dx.doi.org/10.3390/universe7050153.

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With the advent of gravitational wave astronomy and first pictures of the “shadow” of the central black hole of our milky way, theoretical analyses of black holes (and compact objects mimicking them sufficiently closely) have become more important than ever. The near future promises more and more detailed information about the observable black holes and black hole candidates. This information could lead to important advances on constraints on or evidence for modifications of general relativity. More precisely, we are studying the influence of weak teleparallel perturbations on general relativistic vacuum spacetime geometries in spherical symmetry. We find the most general family of spherically symmetric, static vacuum solutions of the theory, which are candidates for describing teleparallel black holes which emerge as perturbations to the Schwarzschild black hole. We compare our findings to results on black hole or static, spherically symmetric solutions in teleparallel gravity discussed in the literature, by comparing the predictions for classical observables such as the photon sphere, the perihelion shift, the light deflection, and the Shapiro delay. On the basis of these observables, we demonstrate that among the solutions we found, there exist spacetime geometries that lead to much weaker bounds on teleparallel gravity than those found earlier. Finally, we move on to a discussion of how the teleparallel perturbations influence the Hawking evaporation in these spacetimes.

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Vegt, Wim. "Single Harmonic Black Holes." European Journal of Engineering Research and Science 5, no. 1 (January 16, 2020): 57–75. http://dx.doi.org/10.24018/ejers.2020.5.1.1714.

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In this New Theory a “Single Harmonic Black Hole” (SHBH) has been considered to be the Gravitational-Electromagnetic Confinement of a Single Harmonic Electromagnetic Field Configuration in which a perfect equilibrium exists between the outward directed electromagnetic radiation pressure and the inward directed Electromagnetic-Gravitational Interaction force densities. This frequency transformation is possible because of the combined Lorentz / Doppler-Effect transformation during the collapse (contraction) of the radiation when the Gravitational Electromagnetic Confinement has been formed (Implosion of Visible Light). Within the scope of this article “Single Harmonic Black Hole” (SHBH) is considered to be any kind of 3-dimensional confined Single Harmonic Electromagnetic Energy. The inner structure of a “SHBH” has been based on a 3-dimensional isotropic equilibrium within the electromagnetic field configuration. This new theory will explain how electromagnetic fields (wave packages) demonstrate inertia, mass and momentum and which forces keep the wave packages together in a way that they can be measured like particles with their own specific mass and momentum. To understand what electromagnetic inertia and the corresponding electromagnetic mass, spin and electric charge is and how the anisotropy of electromagnetic mass, spin and electric charge can be explained and how it has to be defined, a New Theory about “Electromagnetic-Gravitational Interaction” has been developed. The “New Theory” has been based on the fundamental principle of “Perfect Equilibrium within the Universe” which has already been expressed by Newton’s three equations published in 1687 in “Philosophiae Naturalis Principia Mathematica. Newton’s Equations in 3 dimensions will be published in this article in an extension into 4 dimensions. Newton’s 4-dimensional law in the 3 spatial dimensions results in an improved version of the classical Maxwell Equations and Newton’s law in the 4th dimension (time) results in the quantum mechanical Schrödinger wave equation (at non-relativistic velocities) and the relativistic Dirac equation.

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HASAN, M. KHAYRUL. "DISPERSION RELATIONS FOR COLD PLASMA AROUND THE HORIZON OF SCHWARZSCHILD–DE SITTER BLACK HOLE." International Journal of Modern Physics D 19, no. 02 (February 2010): 113–35. http://dx.doi.org/10.1142/s0218271810016270.

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In this paper, we investigate the wave properties of cold plasma in the vicinity of Schawarzchild–de Sitter black hole horizon using 3 + 1 formalism. The general relativistic magnetohydrodynamical equations are formulated for this space–time with the use of Rindler coordinates. We consider both the rotating and nonrotating surroundings with magnetized and nonmagnetized plasmas. Linear perturbation and Fourier analysis techniques are applied by introducing simple harmonic waves. We derive complex dispersion relation from the determinant of Fourier analyzed equations for each case which provides real and complex values of the wave number. From the wave number we determine the phase and group velocities, the refractive index etc., which are used to discuss the characteristics of the waves around the event horizon.

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Sharif, M., and G. Mustafa. "Wave properties of plasma surrounding the event horizon of a nonrotating black hole." Canadian Journal of Physics 86, no. 11 (November 1, 2008): 1265–85. http://dx.doi.org/10.1139/p08-074.

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We study the wave properties of a cold isothermal plasma in the vicinity of a Schwarzschild black-hole event horizon. The Fourier-analyzed perturbed 3+1 general relativistic magnetohydrodynamics equations are examined such that the complex dispersion relations are obtained for nonrotating, rotating nonmagnetized, and rotating magnetized backgrounds. The propagation and attenuation vectors along with the refractive index are obtained (shown graphically) to study the dispersive properties of the medium near the event horizon. The results show that no information can be obtained from the Schwarzschild magnetosphere. Further, the pressure stops the existence of normal dispersion of waves.PACS Nos.: 95.30.Sf, 95.30.Qd, 04.30.Nk

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SMOLLER, JOEL, and BLAKE TEMPLE. "SHOCK WAVE COSMOLOGY INSIDE A BLACK HOLE: THE CASE OF NON-CRITICAL EXPANSION." Journal of Hyperbolic Differential Equations 01, no. 03 (September 2004): 429–43. http://dx.doi.org/10.1142/s0219891604000214.

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We derive and analyze the equations that extend the results in [20,21] to the case of non-critical expansion k≠0. By an asymptotic argument we show that the equation of state [Formula: see text] plays the same distinguished role in the analysis when k≠0 as it does when k=0: only for this equation of state does the shock emerge from the Big Bang at a finite nonzero speed — the speed of light. We also obtain a simple closed system that extends the case [Formula: see text] considered in [20,21] to the case of a general positive, increasing, convex equation of state p=p(ρ).

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MATYJASEK, JERZY, and DARIUSZ TRYNIECKI. "AdS2×S2 GEOMETRIES AND THE EXTREME QUANTUM-CORRECTED BLACK HOLES." Modern Physics Letters A 24, no. 31 (October 10, 2009): 2517–30. http://dx.doi.org/10.1142/s0217732309031910.

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The second-order term of the approximate stress–energy tensor of the quantized massive scalar field in the Bertotti–Robinson and Reissner–Nordström spacetimes is constructed within the framework of the Schwinger–DeWitt method. It is shown that although the Bertotti–Robinson geometry is a self-consistent solution of the (Λ = 0) semiclassical Einstein field equations with the source term given by the leading term of the renormalized stress–energy tensor, it does not remain so when the next-to-leading term is taken into account and requires the introduction of a cosmological term. The addition of the electric charge to the system does not change this behavior. The near horizon geometry of the extreme quantum-corrected Reissner–Nordström black hole is analyzed. It has the AdS2 ×S2 topology and the sum of the curvature radii of the two-dimensional submanifolds is proportional to the trace of the second-order term. It suggests that the "minimal" approximation should be constructed from the first two terms of the Schwinger–DeWitt expansion

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Journal articles on the topic 'Wave equations on black hole spacetimes'

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