Schwarzschild-like Black Hole Research Articles

Gravitational axial perturbations of Schwarzschild-like black holes in dark matter halos

Gravitational waves emitted by distorted black holes, such as those arising from the coalescence of binary black holes, or a falling compact star into a supermassive black hole, carry not only information about the corresponding spacetime but also information about the environment surrounding the black holes. In this paper, we study the effects of the dark matter halos with three different density profiles on the gravitational axial perturbations of a Schwarzschild-like black hole. For this purpose, we first consider modified Schwarzschild black holes with three different dark matter profiles and derive the equation of motion of the axial perturbations of the modified Schwarzschild metric. It is shown that by ignoring the dark matter perturbations, a Regge-Wheeler-like master equation with a modified potential for the axial perturbation can be obtained explicitly. Then we calculate the complex frequencies of the quasi-normal modes of the Schwarzschild-like black hole in the dark matter halos by applying the sixth-order WKB method. The corresponding gravitational wave spectra with the effects of the dark matter halos have also been discussed.

Schwarzschild-like black hole with a topological defect in bumblebee gravity

In this paper, we derive an exact black hole spacetime metric in the Einstein–Hilbert–Bumblebee (EHB) gravity around global monopole field. We study the horizon, temperature, and the photon sphere of the black hole. Using the null geodesics equation, we obtain the shadow cast by the Schwarzschild-like black hole with a topological defect in bumblebee gravity. Interestingly, the radius of shadow of the black hole increases with increase in the global monopole parameter. We also visualize the shadows and energy emission rates for different values of parameters. Moreover, using the Gauss–Bonnet theorem, we calculate the deflection angle in weak field limits and we discuss the possibility of testing the effect of global monopole field and bumblebee field, on a weak deflection angle. We find that the global monopole parameter and also Lorentz symmetry breaking parameter has an increasing effect on the deflection angle.

Scattering by deformed black holes

Obtaining black hole solutions in alternative theories of gravity can be a difficult task due to cumbersome field equations that arise in many of such theories. In order to study the strong field regime in a model-free approach, one can consider deformed black hole solutions with additional parameters beyond mass, charge and angular momentum. We investigate the scattering and absorption of a massless scalar field by non-Schwarzschild black holes, considering the Johannsen and Psaltis parametrization. In particular, we study the scattering process by the classical (null geodesics analysis), semiclassical (glory approximation) and partial waves approaches. We present the formalism needed to compute the scattering and absorption of massless scalar waves by Schwarzschild-like black holes with a set of deformation parameters in addition to their mass and present a selection of our results. We compare our numerical results for the scattering cross section with the classical and semiclassical results, obtaining excellent agreement.

Deformed black hole immersed in dark matter spike

If a lot of dark matter particles accumulate near the black hole, then the chances of detecting dark matter signals near a black hole are greatly increased. These effects may be observed by the Event Horizon Telescope (EHT), Tianqin project, Taiji project, Laser Interferometer Space Antenna (LISA) and Laser Interferometer Gravitational-Wave Observatory (LIGO). In this work, we explore the effects of dark matter spikes on black hole space-time. For the Schwarzschild-like black hole case, we consider Newton's approximation and perturbation approximation. This makes it possible to use Xu's method to solve the Einstein field equation, and extend Schwarzschild-like black hole to Kerr-like black hole (BH) via Newman-Janis (NJ) algorithm. By analyzing the dark matter spike on the black hole event horizon (EH), stationary limit surfaces (SLS), ergosphere and energy-momentum tensors (EMT), we found that compared with the dark matter halo, the dark matter spike would have a higher effect on the black hole by several orders of magnitude. Therefore, if there is a dark matter spike near the black hole, it is very possible to test the dark matter model through gravitational wave (GW) observation and EHT observation.

Circular orbit of a particle and weak gravitational lensing

The purpose of this paper is twofold. First, we introduce a geometric approach to study the circular orbit of a particle in static and spherically symmetric spacetime based on Jacobi metric. Second, we apply the circular orbit to study the weak gravitational deflection of null and time-like particles based on Gauss-Bonnet theorem. By this way, we obtain an expression of deflection angle and extend the study of deflection angle to asymptotically non-flat black hole spacetimes. Some black holes as lens are considered such as a static and spherically symmetric black hole in the conformal Weyl gravity and a Schwarzschild-like black hole in bumblebee gravity. Our results are consistent with the previous literature. In particular, we find that the connection between Gaussian curvature and the radius of a circular orbit greatly simplifies the calculation.

Thermodynamics of Schwarzschild-like black holes in modified gravity models

Over the last decades, many methods were developed to prove Hawking radiation. Recently, a semiclassical method known as the tunneling method has been proposed as a more straightforward way of derivating black hole thermodynamical properties. This method has been widely applied to a vast sort of spacetimes with satisfactory results. In this work, we obtain the black hole thermodynamics in the presence of a Lorentz symmetry breaking (LSB). We apply the Hamilton–Jacobi method to Schwarzschild-like black holes, and we investigate whether the LSB affects their thermodynamics. The results found show that the LSB not only changes the black hole thermodynamic quantities but also makes it necessary to modify the standard first law of thermodynamics.

Black hole immersed dark matter halo

In this work, based on the constant for the equation of state $\ensuremath{\omega}$, we obtain the Schwarzschild-like black hole solutions in some dark matter halos. We also generalize these black hole metrics to Kerr-like black hole solutions with Newman-Janis algorithm. For an example, we derive the specific black hole space-time metrics in the case of the cold dark matter halo and Bose-Einstein condensation dark matter halo. Following the above two black hole metrics, we discuss how a dark matter halo changes the properties of black holes, including the event horizon structure (these results agree with that obtained by Liu and Zhang [Phys. Lett. B 679, 88 (2009).] in the case of gravitational collapse), stationary limit surfaces, ergosphere, and singularity structure. Our results may help us understand the interaction between the dark matter halo and supermassive black holes at the centers of galaxies.

GUP modified Hawking radiation in bumblebee gravity

The effect of Lorentz symmetry breaking (LSB) on the Hawking radiation of Schwarzschild-like black hole found in the bumblebee gravity model (SBHBGM) is studied in the framework of quantum gravity. To this end, we consider Hawking radiation spin-0 (bosons) and spin-12 particles (fermions), which go in and out through the event horizon of the SBHBGM. We use the modified Klein-Gordon and Dirac equations, which are obtained from the generalized uncertainty principle (GUP) to show how Hawking radiation is affected by the GUP and LSB. In particular, we reveal that, independent of the spin of the emitted particle, GUP causes a change in the Hawking temperature of the SBHBGM. Furthermore, we compute the semi-analytic greybody factors (for both bosons and fermions) of the SBHBGM. Thus, we reveal that LSB is effective on the greybody factor of the SBHBGM such that its redundancy decreases the value of the greybody factor. Our findings are graphically depicted.

Effects of Lorentz Breaking on the Accretion onto a Schwarzschild-like Black Hole**Supported by National Natural Science Foundation of China under Grant No. 11273010; the Hebei Provincial Outstanding Youth Fund under Grant No. A2014201068; the Outstanding Youth Fund of Hebei University under Grant No. 2012JQ02; and the Midwest Universities Comprehensive Strength Promotion Project

We formulate and solve the problem of spherically symmetric, steady state, adiabatic accretion onto a Schwarzschild-like black hole obtained recently. We derive the general analytic expressions for the critical points, the critical velocity, the critical speed of sound, and subsequently the mass accretion rate. The case for polytropic gas is discussed in detail. We find the parameter characterizing the breaking of Lorentz symmetry will slow down the mass accretion rate, while has no effect on the gas compression and the temperature profile below the critical radius and at the event horizon.

Gravitational lensing under the effect of Weyl and bumblebee gravities: Applications of Gauss–Bonnet theorem

In this paper, we use the Gauss–Bonnet theorem to obtain the deflection angle by the photons coupled to Weyl tensor in a Schwarzschild black hole and Schwarzschild-like black hole in bumblebee gravity in the weak limit approximation. To do so, we first calculate the corresponding optical metrics, and then we find the Gaussian curvature to use in Gauss–Bonnet theorem, which is first done by Gibbons and Werner. Hence, in the leading order terms we show the deflection angle, that is affected by the coupling between the photon and Weyl tensor, and there is a deviation from the deflecting angle as compared with Schwarzschild black hole with Schwarzschild-like black hole in bumblebee gravity. Moreover, we investigate the deflection angle by Einstein–Rosen type wormhole in Weyl gravity and in bumblebee gravity. Interestingly, the deflection angle by Einstein–Rosen type wormhole in bumblebee gravity is found as larger than the deflection angle by Einstein–Rosen type wormhole in Weyl gravity.

Exact Solution for a Black Hole Embedded in a Nonstatic Dust-filled Universe

Abstract An exact solution of the Lemaître–Tolman–Bondi class is investigated as a possible model of the Schwarzschild-like black hole embedded in a nonstatic dust-filled universe for the three types of spatial curvature. The solution is obtained in comoving coordinates by means of the mass function method. It is shown that the central part of space contains a Schwarzschild-like black hole. The R–T structure of the resulting spacetime is built. It is shown that the solution includes both the Schwarzschild and Friedmann solutions as its natural limits. The geodesic equations for test particles are analyzed. The particle observable velocities are found. The trajectories of the test particles are built from the point of view of both comoving and distant observers. For the distant observer, the results coincide with the Schwarzschild picture within a second-order accuracy near the symmetry center.

Reentrant phase transition of Born-Infeld-AdS black holes

We investigate thermodynamic phase structure and critical behaviour of Born-Infeld (BI) black holes in an anti-de Sitter (AdS) space, where the charge of the system can vary and the cosmological constant (pressure) is fixed. We find that the BI parameter crucially affects the temperature of the black hole when the horizon radius, $r_{+}$, is small. We observe that depending on the value of the nonlinear parameter, $\beta $, BI-AdS black hole may be identified as RN black hole for $Q\geq Q_{m}$, and Schwarzschild-like black hole for $Q<Q_{m}$, where $Q_{m}=1/\left(8\pi \beta \right) $ is the \textit{marginal} charge. We analytically calculate the critical point ($% Q_c,T_c, r_{+c}$) by solving the cubic equation and study the critical behaviour of the system. We also explore the behavior of Gibbs free energy for BI-AdS black hole. We find out that the phase behaviour of BI-AdS black hole depends on the charge $Q$. For $Q>Q_{c}$, the Gibbs free energy is single valued and the system is locally stable ($C_{Q}>0$), while for $% Q<Q_{c}$, it becomes multivalued and $C_{Q}<0$. In the range of $% Q_{z}<Q<Q_{c}$, a first order phase transition occurs between small black hole (SBH) and large black hole (LBH). Interestingly enough, in the range of $Q_{t}\leq Q\leq Q_{z}$, a reentrant phase transition occurs between intermediate (large) black hole, SBH and LBH in Schwarzschild-type region. This means that in addition to the first order phase transition which separates SBH and LBH, a finite jump in Gibbs free energy leads to a \textit{% zeroth order} phase transition between SBH and intermediate black hole (LBH) where initiates from $Q=Q_{z}$ and terminates at $Q=Q_{t}$.

Exact Schwarzschild-like solution in a bumblebee gravity model

We have obtained an exact vacuum solution from a gravity sector contained in the minimal standard-model extension. The theoretical model assumes a Riemann spacetime coupled to the bumblebee field which is responsible for the spontaneous Lorentz symmetry breaking. The solution achieved in a static and spherically symmetric scenario establishes a Schwarzschild-like black hole. In order to study the effects of the spontaneous Lorentz symmetry breaking, we have investigated some classics tests including the advance of the perihelion, bending of light and Shapiro's time-delay. Furthermore, we have computed some upper-bounds from which the most stringent one attains a sensitivity at the $10^{-13}$ level.

Thermodynamic metric of deformed Schwarzschild black holes

Thermodynamic metric usually works only for those black holes with more than one conserved charge, thereby excluding the Schwarzschild black hole. In this paper, however, different versions of thermodynamic metric are computed and compared for the Schwarzschild-like black hole by introducing new degrees of freedom. These new degrees of freedom have two purposes. First, the deformed metric may be treated offshell to the ordinary Schwarzschild black hole, and onshell physics corresponds to the submanifold by gauge fixing of this additional degree of freedom. In particular, the thermal Ricci scalar for the Schwarzschild black hole, though different for various deformations, can be obtained by switching off the deformation. Second, while deformed metric is treated onshell, a divergent Ricci scalar may signal an exotic phase in which new physical degrees of freedom manifest. This paper considers the new degree of freedom as the running Newton constant, a cutoff scale for regular black holes, a noncommutative deformation or the deformed parameter in the nonextensive Tsallis–Rènyi entropy.

Unscreening scalarons with a black hole

It is typically believed that the additional degrees of freedom in any modification of gravity are completely suppressed by the large energy densities coexisting with an astrophysical black hole. In this paper, we find that this might not always be the case. This belief holds for black holes formed via gravitational collapse in very dense environments, whereas the black holes with sufficiently low accretion rates that have low matter densities inside innermost stable circular orbit will generally unscreen chameleons. We develop a novel technique to study the dynamics of accretion of a scalar field onto a Schwarzschild-like black hole which is accurate on both short and long time scales. In particular, we study the behavior of the extra scalar degree of freedom in the Starobinsky and Hu-Sawicki $f(R)$ theories, for the symmetron model, and for the Ratra-Peebles model. Aside from calculating non-trivial static field profiles outside the black hole, we provide the tools to study the (in)stability and evolution towards the equilibrium solution for any generic well behaved set of parameters and initial conditions. Our code is made publicly available for further research and modifications to study other models.

Regular black holes and noncommutative geometry inspired fuzzy sources

We investigated regular black holes with fuzzy sources in three and four dimensions. The density distributions of such fuzzy sources are inspired by noncommutative geometry and given by Gaussian or generalized Gaussian functions. We utilized mass functions to give a physical interpretation of the horizon formation condition for the black holes. In particular, we investigated three-dimensional BTZ-like black holes and four-dimensional Schwarzschild-like black holes in detail, and found that the number of horizons is related to the space–time dimensions, and the existence of a void in the vicinity of the center of the space–time is significant, rather than noncommutativity. As an application, we considered a three-dimensional black hole with the fuzzy disc which is a disc-shaped region known in the context of noncommutative geometry as a source. We also analyzed a four-dimensional black hole with a source whose density distribution is an extension of the fuzzy disc, and investigated the horizon formation condition for it.

Strong gravitational lensing by Kiselev black hole

We investigate the gravitational lensing scenario due to Schwarzschild-like black hole surrounded by quintessence (Kiselev black hole). We work for the special case of Kiselev black hole where we take the state parameter $w_{q}=-\frac{2}{3}$. For the detailed derivation and analysis of the bending angle involved in the deflection of light, we discuss three special cases of Kiselev black hole: non-extreme, extreme and naked singularity. We also calculate the approximate bending angle and compare it with exact bending angle. We found the relation of bending angles in the decreasing order as: naked singularity, extreme Kiselev black hole, non-extreme Kiselev black hole and Schwarzschild black hole. In the weak field approximation, we compute the position and total magnification of relativistic images as well.

Dynamics of particles around a Schwarzschild-like black hole in the presence of quintessence and magnetic field

We investigate the dynamics of a neutral and a charged particle around a static and spherically symmetric black hole in the presence of quintessence matter and external magnetic field. We explore the conditions under which the particle moving around the black hole could escape to infinity after colliding with another particle. The innermost stable circular orbit (ISCO) for the particles are studied in detail. Mainly the dependence of ISCO on dark energy and on the presence of external magnetic field in the vicinity of black hole is discussed. By using the Lyapunov exponent, we compare the stabilities of the orbits of the particles in the presence and absence of dark energy and magnetic field. The expressions for the center of mass energies of the colliding particles near the horizon of the black hole are derived. The effective force on the particles due to dark energy and magnetic field in the vicinity of black hole is also discussed.

Thermodynamic analysis of black hole solutions in gravitating nonlinear electrodynamics

We perform a general study of the thermodynamic properties of static electrically charged black hole solutions of nonlinear electrodynamics minimally coupled to gravitation in three space dimensions. The Lagrangian densities governing the dynamics of these models in flat space are defined as arbitrary functions of the gauge field invariants, constrained by some requirements for physical admissibility. The exhaustive classification of these theories in flat space, in terms of the behaviour of the Lagrangian densities in vacuum and on the boundary of their domain of definition, defines twelve families of admissible models. When these models are coupled to gravity, the flat space classification leads to a complete characterization of the associated sets of gravitating electrostatic spherically symmetric solutions by their central and asymptotic behaviours. We focus on nine of these families, which support asymptotically Schwarzschild-like black hole configurations, for which the thermodynamic analysis is possible and pertinent. In this way, the thermodynamic laws are extended to the sets of black hole solutions of these families, for which the generic behaviours of the relevant state variables are classified and thoroughly analyzed in terms of the aforementioned boundary properties of the Lagrangians. Moreover, we find universal scaling laws (which hold and are the same for all the black hole solutions of models belonging to any of the nine families) running the thermodynamic variables with the electric charge and the horizon radius. These scale transformations form a one-parameter multiplicative group, leading to universal "renormalization group"-like first-order differential equations. The beams of characteristics of these equations generate the full set of black hole states associated to any of these gravitating nonlinear electrodynamics...

Energy and Momentum of Higher Dimensional Black Holes

In this paper, we devote to investigate the energy-momentum problem of higher dimensional black holes in the general theory of relativity. The energy and momentum complex of Moller has been used for the calculations. Also, total energy and total momentum of some special cases for higher dimensional black holes such as Schwarzschild-like black holes, Reissner-Nordstrom-like charged black holes, AdS-like black holes, topological black holes, BTZ-like and charged BTZ-like black holes were obtained. It is invented that the momentum of black holes vanishes everywhere while the energy of black holes are not equal to zero in higher dimension. Also the results agree with Yang and Radinschi or Vagenas results in three and four dimensional black holes, respectively (Jang and Radinschi in AIP Conf. Proc. 895, 325, 2007; Vagenas in Mod. Phys. Lett. A 21, 1947, 2006).