Black Holes In General Relativity Research Articles

Gravitational lensing by charged black hole in regularized 4D Einstein\u2013Gauss\u2013Bonnet gravity

Among the higher curvature gravities, the most extensively studied theory is the so-called Einstein–Gauss–Bonnet (EGB) gravity, whose Lagrangian contains Einstein term with the GB combination of quadratic curvature terms, and the GB term yields nontrivial gravitational dynamics in Dge 5. Recently there has been a surge of interest in regularizing, a D rightarrow 4 limit of, the EGB gravity, and the resulting regularized 4D EGB gravity valid in 4D. We consider gravitational lensing by Charged black holes in the 4D EGB gravity theory to calculate the light deflection coefficients in strong-field limits bar{a} and bar{b}, while former increases with increasing GB parameter alpha and charge q, later decrease. We also find a decrease in the deflection angle alpha _D, angular position theta _{infty } decreases more slowly and impact parameter for photon orbits u_{m} more quickly, but angular separation s increases more rapidly with alpha and charge q. We compare our results with those for analogous black holes in General Relativity (GR) and also the formalism is applied to discuss the astrophysical consequences in the case of the supermassive black holes Sgr A* and M87*.

Testing horizon topology with electromagnetic observations

In general relativity without a cosmological constant, a classical theorem due to Hawking states that stationary black holes must be topologically spherical. This result is one of the several ingredients that collectively imply the uniqueness of the Kerr metric. If, however, general relativity describes gravity inexactly at high energies or over cosmological scales, Hawking's result may not apply, and black holes with non-trivial topology may be, at least mathematically, permissible. While tests involving electromagnetic and gravitational-wave data have been used to place tight constraints on various theoretical departures from a Kerr description of astrophysical black holes, relatively little attention has been paid to topological alternatives. In this paper, we derive a new exact solution in an $f(R)$ theory of gravity which admits topologically non-trivial black holes, and calculate observables like fluorescent K$\alpha$ iron-line profiles and black hole images from hypothetical astrophysical systems which house these objects, to provide a theoretical basis for new tests of black hole nature. On the basis of qualitative comparisons, we show that topologically non-trivial objects would leave a strong imprint on electromagnetic observables and can be easily distinguished from general-relativistic black holes in nearly all cases.

Regular multihorizon black holes in general relativity

In this work, new solutions for regular black holes that have multihorizons are proposed. These are formed by the direct product of solutions already published in the literature, which are described through the coupling of gravity with nonlinear electrodynamics. We analyze the regularity of the spacetime, the electric field, and the energy conditions of each solution. The strong energy condition is always violated within the event horizon in all solutions, while other energy conditions depend on the ratio between extreme charges of isolated solutions. For solutions with four horizons, we present two examples, Bardeen-Culetu and Balart-Culetu. Both solutions are regular, but the first do not satisfy all the energy conditions, except the strong, because it has an extreme charge ratio of 1.57581, great value. The second solution, on the other hand, can satisfy all other energy conditions, except the SEC, and has an extreme charge ratio of 1.09915, a value that allows this feature. It's also proposed a regular solution with up to six horizons, Balart-Culetu-Dymnikova, where, for a given charge value, we can verify that it satisfies all energy conditions, except the strong one. This was possible due to the ratio between extreme charges that are neither too high nor too close. We propose solutions with any number of horizons. We show that points where $-F(r)$ has a non null minimum represent a cusp in the Lagrangian $-L(F)$. We also show an example of multihorizon solution with magnetic charge. Multihorizon solutions may exhibit exotic properties, such as negative energy density, or violation of energy conditions, but which can be circumvented with a selected choice of customized solutions and extreme charge values, resulting in regular black hole solutions that satisfy all energy conditions, less the strong.

Quasi-normal modes of near-extremal black holes in generalized spherically symmetric spacetime and strong cosmic censorship conjecture

A number of near-extremal conditions are utilized to simplify the equation of motion of the neutral scalar perturbations in generalized spherically symmetric black hole background into a differential equation with the Pöschl–Teller potential. An analytic formula for quasinormal frequencies is obtained. The analytic formula is then used to investigate strong cosmic censorship conjectures (SCC) of the generalized black hole spacetime for the smooth initial data. The Christodoulou version of the SCC is found to be violated for certain regions of the black hole parameter space including the black holes in general relativity while the C^{1} version of the SCC is always valid.

Critical behaviors of a (2 + 1)-dimensional black hole with a nonlinear electrodynamics source

On the basis of a charged BTZ black hole, we add an extra term in the metric function to describe the contribution from nonlinear electrodynamics. In this way we artificially construct a (2 + 1)-dimensional black hole in general relativity coupled with a nonlinear electrodynamics source. The thermodynamic quantities and Smarr formula are derived. It is found that this black hole has T − S criticality like that of an RN-AdS black hole. Further modifying the metric function, we obtain a (2 + 1)-dimensional black hole possessing P − V critical behaviors similar to that of van der Waals fluid. To our knowledge, this is the first example of (2 + 1)-dimensional black holes having this kind of critical behavior.

Optical properties of Kerr–Newman spacetime in the presence of plasma

We have studied the null geodesics in the background of the Kerr–Newman black hole veiled by a plasma medium using the Hamilton–Jacobi method. The influence of black hole’s charge and plasma parameters on the effective potential and the generic photon orbits has been investigated. Furthermore, our discussion embodies the effects of black hole’s charge, plasma and the inclination angle on the shadow cast by the gravity with and without the spin parameter. We examined the energy released from the black hole as a result of the thermal radiations, which exclusively depends on the size of the shadow. The angle of deflection of the massless particles is also explored considering a weak-field approximation. We present our results in juxtaposition to the analogous black holes in General Relativity, particularly the Schwarzschild and Kerr black hole.

Radiating black holes in the novel 4D Einstein–Gauss–Bonnet gravity

Recently Glavan and Lin (2020) formulated a novel Einstein–Gauss–Bonnet gravity in which the Gauss–Bonnet coupling has been rescaled as α∕(D−4) and the 4D theory is defined as the limit D→4, which preserves the number degrees of freedom thereby free from the Ostrogradsky instability. We present exact spherically symmetric nonstatic null dust solutions in the novel 4D Einstein–Gauss–Bonnet gravity that bypasses the Lovelock theorem. Our solution represents radiating black holes and regains, in the limit α→0, the famous Vaidya black hole of general relativity (GR). We discuss the horizon structure of black hole solutions to find that the three horizon-like loci that characterizes its structure, viz. AH, EH and TLS have the relationship rEH<rAH=rTLS. The charged radiating black holes in the theory, generalizing Bonnor–Vaidya black holes, are also considered. In particular our results, in the limit α→0, reduced exactly to vis-à-vis 4D black holes of GR.

Test particle orbits around regular black holes in general relativity combined with nonlinear electrodynamics

We provide detailed analysis of the curvature structure of the spacetime around regular black holes (RBHs) governed by general relativity (GR) combined with nonlinear electrodynamics (NED), characterized by electric charge $Q$, and degree of nonlinearity $n$. We consider special class of the backgrounds introduced by Toshmatov et al. [Phys. Rev. D 98, 028501 (2018)] that have proper Maxwell weak-field limit of the NED sector. We also study the motion of uncharged and charged particles in the RBH background. We determine shadows of such black holes (BHs) using the effective geometry governing motion of photons in the background of NED RBHs. The analysis of circular motion enables to determine innermost stable circular orbits (ISCO) and marginally bound orbits (MBO). We show that the radius of ISCO and MBO for neutral particles decreases as the parameters of the RBH $Q$ and $n$ increase for the fixed value of the BH mass. We demonstrate that for the electrically charged particles properties of the circular orbits strongly depend on their Coulomb interaction with the RBH charge. The dependence of the ISCO radius on the particle specific charge $q$ and the RBH parameters is rather complex, but for the attractive Coulomb interaction there is a general feature (independent of $n$) giving a limiting value of the intensity of this interaction $q{Q}_{\mathrm{max}}$ behind which no stable circular orbits are allowed around the RBH. Comparison of the RBH with Reissner-Nordstr\"om black holes (RNBH) shows that for the same electric charges of these backgrounds the location of the relevant orbits is at substantially smaller radii for the RBH, demonstrating thus a strong influence of the NED effects. The analysis of ISCO radius of test particles has shown that the charge of RBH $Q$ can mimic the rotation parameter of Kerr BH up to the value $a=0.8M$. We have also shown that the RN BH charge can mimic the rotation parameter up to $a=0.5M$ and the RBH charge up to $Q=0.2M$. Applications from observational data to the parameters of the supermassive black holes (SMBHs) at the galactic center Messier 87 (M87) and Milky Way so called Sagittarius ${\mathrm{A}}^{*}$ (${\mathrm{Sgr}\text{ }A}^{*}$) give the mimic value for the RBH charge parameter for the rotation parameter of M87 to be ${10}^{3}Q\ensuremath{\approx}277.5{6}_{\ensuremath{-}1.26}^{+3.82}$, while for ${\mathrm{Sgr}\text{ }A}^{*}$ there is ${10}^{3}Q\ensuremath{\approx}187.3{3}_{\ensuremath{-}26.4}^{+27.6}$. Moreover, it is shown that the RN BH charge cannot mimic the rotation parameter of the SMBH M87, however, it can mimic the spin parameter of ${\mathrm{Sgr}\text{ }A}^{*}$ at ${10}^{3}{Q}_{\mathrm{RN}}/M=828.7{1}_{\ensuremath{-}60.94}^{+70.58}$.

Probing beyond-Kerr spacetimes with inspiral-ringdown corrections to gravitational waves

Gravitational waves from the explosive merger of distant black holes are encoded with details regarding the complex extreme-gravity spacetime present at their source. Famously described by the Kerr spacetime metric for rotating black holes in general relativity, what if effects beyond this theory are present? One way to efficiently test this hypothesis is to first obtain a metric which parametrically deviates from the Kerr metric in a model-independent way. Given such a metric, one can then predict the ensuing corrections to both the inspiral and ringdown portions of the gravitational waveform for black holes present in the new spacetime. With these tools in hand, one can then test gravitational wave signals for such effects by two different methods, (i) inspiral-merger-ringdown consistency test, and (ii) parameterized test. In this paper, we demonstrate the exact recipe one needs to do just this. We first derive parameterized corrections to the waveform inspiral, ringdown, and remnant properties for a generic non-Kerr spacetime and apply this to two example beyond-Kerr spacetimes each parameterized by a single non-Kerr parameter. We then predict the beyond-Kerr parameter magnitudes required in an observed gravitational wave signal to be statistically inconsistent with the Kerr case in general relativity. We find that the two methods give very similar bounds. The constraints found with existing gravitational-wave events are comparable to those from x-ray observations, while future gravitational-wave observations using Cosmic Explorer (Laser Interferometer Space Antenna) can improve such bounds by two (three) orders of magnitude.

Black holes in self-tuning cubic Horndeski cosmology

Observations of neutron star mergers in the late Universe have given significant restrictions to the class of viable scalar-tensor theories. In this paper we construct black holes within the "self-tuning" class of this restricted set, whereby the bare cosmological constant is absorbed by the dynamics of the scalar, giving a lower effective cosmological constant. We use analytic expansions at the singularity, black hole and cosmological horizon, and asymptotic region, coupled with numerical solutions, to find well-behaved black holes that asymptote to the self-tuned de Sitter geometry. The geometry differs from standard general relativity black holes near the horizon, and the scalar field velocity provides a hair for the black holes.

Black Hole Parameter Estimation from Its Shadow

Abstract The Event Horizon Telescope (EHT), a global submillimeter wavelength very long baseline interferometry array, unveiled event-horizon–scale images of the supermassive black hole M87* as an asymmetric bright emission ring with a diameter of 42 ± 3 μas, and it is consistent with the shadow of a Kerr black hole of general relativity. A Kerr black hole is also a solution of some alternative theories of gravity, while several modified theories of gravity admit non-Kerr black holes. While earlier estimates for the M87* black hole mass, depending on the method used, fall in the range , the EHT data indicated a mass for the M87* black hole of (6.5 ± 0.7) × 109 M ⊙. This offers another promising tool to estimate black hole parameters and to probe theories of gravity in its most extreme region near the event horizon. The important question arises: Is it possible by a simple technique to estimate black hole parameters from its shadow, for arbitrary models? In this paper, we present observables, expressed in terms of ordinary integrals, characterizing a haphazard shadow shape to estimate the parameters associated with black holes, and then illustrate its relevance to four different models: Kerr, Kerr–Newman, and two rotating regular models. Our method is robust, accurate, and consistent with the results obtained from existing formalism, and it is applicable to more general shadow shapes that may not be circular due to noisy data.

Test black holes, scattering amplitudes, and perturbations of Kerr spacetime

It has been suggested that amplitudes for quantum higher-spin massive particles exchanging gravitons lead, via a classical limit, to results for scattering of spinning black holes in general relativity, when the massive particles are in a certain way minimally coupled to gravity. Such limits of such amplitudes suggest, at least at lower orders in spin, up to second order in the gravitational constant $G$, that the classical aligned-spin scattering function for an arbitrary-mass-ratio two-spinning-black hole system can be obtained by a simple kinematical mapping from that for a spinning test black hole scattering off a stationary background Kerr black hole. Here we test these suggestions, at orders beyond the reach of the post-Newtonian and post-Minkowskian results used in their initial partial verifications, by confronting them with results from general-relativistic ``self-force'' calculations of the linear perturbations of a Kerr spacetime sourced by a small orbiting body, here considering only results for circular orbits in the equatorial plane. We translate between scattering and circular-orbit results by assuming the existence of a local-in-time canonical Hamiltonian governing the conservative dynamics of generic (bound and unbound) aligned-spin orbits, while employing the associated first law of spinning binary mechanics. To the extent possible with available self-force results, we confirm, through linear order in the mass ratio, some previous conjectures which would begin to fill in the spin-dependent parts of the conservative dynamics for arbitrary-mass-ratio aligned-spin binary black holes at the fourth-and-a-half and fifth post-Newtonian orders.

Environmental effects in gravitational-wave physics: Tidal deformability of black holes immersed in matter

The tidal deformability of compact objects by a companion has a detectable imprint in the gravitational waves emitted by a binary system. This effect is governed by the so-called tidal Love numbers. For a particular theory of gravity, these depend solely on the object internal structure and they vanish for black holes in general relativity. A measurement compatible with nonzero tidal Love numbers could thus provide evidence of new physics in the strong-field regime. However, in realistic astrophysical scenarios, compact objects are surrounded by a nonvacuum environment. In this work, we study the tidal deformability of configurations of black holes immersed in matter, focusing on two analytical models representing an anisotropic fluid and a thin-shell of matter around a black hole. We then apply our results to the astrophysically relevant case of a black hole surrounded by an accretion disk, in the parameter region of interest of the upcoming LISA mission. Our results indicate that there are challenges to overcome concerning tests of strong-field gravity using tidal Love numbers.

Observational signature of a near-extremal Kerr-Sen black hole in the heterotic string theory

We analytically study the optical appearance of an isotropically emitter orbiting near the horizon of a near-extremely rotating Kerr-Sen (KS) black hole which is an electrically charged black hole arising in heterotic string theory. We study the influence of the Sen charge on the observational quantities, including the image position, flux and redshift factor. Moreover, we compare the results with those for a near-extremal Kerr-Newman (KN) black hole, which is the charged rotating black hole in general relativity. We find quantitative corrections of the signatures of these charged black holes (both KS and KN) compare to that of a neutral Kerr black hole. This may serve as distinctive features of different black holes for future tests by the Event Horizon Telescope.

Testing the no-hair nature of binary black holes using the consistency of multipolar gravitational radiation

Gravitational-wave (GW) observations of binary black holes offer the best probes of the relativistic, strong-field regime of gravity. Gravitational radiation, in the leading order is quadrupolar. However, non-quadrupole (higher-order) modes make appreciable contribution to the radiation from binary black holes with large mass ratios and misaligned spins. The multipolar structure of the radiation is fully determined by the intrinsic parameters (masses and spin angular momenta of the companion black holes) of a binary in quasi-circular orbit. Following our previous work \cite{Dhanpal:2018ufk}, we develop multiple ways of testing the consistency of the observed GW signal with the expected multipolar structure of radiation from binary black holes in general relativity. We call this a "no-hair" test of binary black holes as this is similar to testing the "no-hair" theorem for isolated black holes through mutual consistency of the quasi-normal mode spectrum. We use Bayesian inference on simulated GW signals that are consistent/inconsistent with binary black holes in GR to demonstrate the power of the proposed tests. We also make estimate systematic errors arising as a result of neglecting companion spins.

Reply to “Comment on ‘Boosted Kerr black holes in general relativity”’

We discuss the comments made by Emanuel Gallo and Thomas M\adler on our papers [Gen. Relativ. Gravit. 49, 77 (2017) and Phys. Rev. D 99, 084054 (2019)] on boosted Kerr black holes in general relativity. We considered their criticisms carefully, as they added a significant contribution to the question of boosted Kerr black holes in general relativity examined in our papers. Here, we expand on further results of our papers that were not duly included in the published papers, as noticed by Gallo and M\adler. We now consider the complete asymptotic Lorentz transformations of Robinson-Trautman (RT) coordinates to Bondi-Sachs (BS) asymptotic coordinates of a radiative RT spacetime, which include the perturbation term of the boosted RT metric corresponding to the Lense-Thirring rotation originating from the Kerr metric. The transformation of the rotation parameter $\ensuremath{\omega}$ as the RT coordinates transform to BS coordinates is obtained, as well as the form of the boosted Kerr metric where we make use of the complete asymptotic Lorentz transformation.

Comment on “Boosted Kerr black holes in general relativity”

We discuss a recently presented boosted Kerr black hole solution which had already been used by other authors. This boosted metric is based on wrong assumptions regarding asymptotic inertial observers and moreover the performed boost is not a proper Lorentz transformation. This note aims to clarify some of the issues when boosting black holes and the necessary care in order to interpret them. As it is wrongly claimed that the presented boosted Kerr metric is of Bondi-Sachs type, we recall out some of the necessary requirements and difficulties, when the casting the Kerr metric into a metric with a surface forming null coordinate.

Constructing black hole solutions in supergravity theories

We perform a detailed analysis of black hole solutions in supergravity models. After a general introduction on black holes in general relativity and supersymmetric theories, we provide a detailed description of ungauged extended supergravities and their dualities. Therefore, we analyze the general form of black hole configurations for these models, their near-horizon behavior and characteristic of the solution. An explicit construction of a black hole solution with its physical implications is given for the STU-model. The second part of this review is dedicated to gauged supergravity theories. We describe a step-by-step gauging procedure involving the embedding tensor formalism to be used to obtain a gauged model starting from an ungauged one. Finally, we analyze general black hole solutions in gauged models, providing an explicit example for the [Formula: see text], [Formula: see text] case. A brief review on special geometry is also provided, with explicit results and relations for supersymmetric black hole solutions.

Mass Evolution of Schwarzschild Black Holes

In the classical theory of general relativity black holes can only absorb and not emit particles. When quantum mechanical effects are taken into account, then the black holes emit particles as hot bodies with temperature proportional to $\kappa$, its surface gravity. This thermal emission can lead to a slow decrease in the mass of the black hole, and eventually to its disappearance, also called black hole evaporation. This characteristic allows us to analyze what happens with the mass of the black hole when its temperature is increased or decreased, and how the energy is exchanged with the external environment. This paper has the aim to make a review about the mass evolution of Schwarzschild black holes with different initial masses and external conditions as the empty space, the cosmic microwave background with constant temperature, and with temperature varying in accordance with the eras of the universe. As a result, we have the complete evaporation of the black holes in most cases, although their masses can increase in some cases, and even diverge for specific conditions.

Strong gravity signatures in the polarization of gravitational waves

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.