Black holes: a physical route to the Kerr metric

As a consequence of Birkhoff's theorem, the exterior gravitational field of a spherically symmetric star or black hole is always given by the Schwarzschild metric. In contrast, the exterior gravitational field of a rotating (axisymmetric) star differs, in general, from the Kerr metric, which describes a stationary, rotating black hole. In this paper I discuss the possibility of a quasi–stationary transition from rotating equilibrium configurations of normal matter to rotating bla ck holes.     

Tachyons in general relativity

The tachyonic version of the Schwarzschild (bradyonic) gravitational field within the framework of extended relativity is considered. The metric of a tachyonic black hole is obtained through superluminal transformations from a bradyonic metric. The extended space-time manifold of this geometry which includes both black and white tachyonic holes is analysed, and the differences between the tachyonic and bradyonic versions are noted. It is shown that the meanings of black holes, tachyons and bradyons depend on the character of the reference frame and are not absolute.     

Robinson-Trautman equations and Chandrasekhar's special perturbation of the Schwarzschild metric

A perturbation wave solution of the Robinson-Trautman equations is proved to be a perturbation of the Schwarzschild black hole which describes an outgoing axial gravitational wave and corresponds to a special case of Chandrasekhar's algebraically special perturbation of the Schwarzschild metric.     

Cold plasma dispersion relations in the vicinity of a Schwarzschild black hole horizon

We apply the ADM 3 + 1 formalism to derive the general relativistic magnetohydrodynamic equations for cold plasma in spatially flat Schwarzschild metric. Respective perturbed equations are linearized for non-magnetized and magnetized plasmas both in non-rotating and rotating backgrounds. These are then Fourier analyzed and the corresponding dispersion relations are obtained. These relations are discussed for the existence of waves with positive angular frequency in the region near the horizon. Our results support the fact that no information can be extracted from the Schwarzschild black hole. It is concluded that negative phase velocity propagates in the rotating background whether the black hole is rotating or non-rotating.     

How black holes form in high energy collisions

Abstract We elucidate how black holes form in trans-Planckian collisions. In the rest frame of one of the incident particles, the gravitational field of the other, which is rapidly moving, looks like a gravitational shock wave. The shock wave focuses the target particle down to a much smaller impact parameter. In turn, the gravitational field of the target particle captures the projectile when the resultant impact parameter is smaller than its own Schwarzschild radius, forming a black hole. One can deduce this by referring to the original argument of escape velocities exceeding the speed of light, which Michell and Laplace used to discover the existence of black holes. Second Award in the 2007 Essay Competition of the Gravity Research Foundation.     

Note on the motion of black holes

It is shown that from the point of view of a distant observer the gravitational field of a moving Schwarzschild black hole is the same as produced by an extended, non-rotating, spherical body of the same mass. According to him, a black hole follows the Newtonian equations of motion, though some quantities, for example the distance, lose their Newtonian meaning.     

Gravitational field in a collision of two Schwarzschild black holes

This paper presents an analysis of the linearized Einstein equations in vacuum for the problem of head-on collision of two Schwarzschild black holes, of which one is much smaller than the other. Based on the decomposition of the metric perturbations into spherical harmonics, introduced by Regge and Wheeler, we give some time-symmetric initial data and calculate the subsequent time-evolution of gravitational field. It is found that the small hole, initially at rest, begins to move like a freely falling particle. A wave-like disturbance generated near the small hole grows up and propagates in the direction opposite to the hole's motion. We investigate the area of the large Schwarzschild horizon distorted by the small hole to obtain the rate of increase with time.     

Letter: A Moving Medium Simulation of Schwarzschild Black Hole Optics

An explicit fluid flow simulation of electromagnetic wave propagation in the gravitational field of a Schwarzschild black hole is given. The fluid has a constant refractive index and a spherically symmetric inward directed flow. The resulting form of the metric leads to a new coordinate system in which the Schwarzschild vacuum is written in Gordon's form. It is shown that a closely related coordinate system interpolates between the Kerr-Schild and Painlevé-Gullstrand coordinates.     

Pair production by gravitational waves in the field of a black hole

We consider the production of scalar particles by a gravitational wave incident on the static gravitational field of a Schwarzschild mini black hole.     

Exact Harmonic Metric for a Uniformly Moving Schwarzschild Black Hole

The harmonic metric for Schwarzschild black hole with a uniform velocity is presented. In the limit of weak field and low velocity, this metric reduces to the post-Newtonian approximation for one moving point mass. As an application, we derive the dynamics of particle and photon in the weak-field limit for the moving Schwarzschild black hole with an arbitrary velocity. It is found that the relativistic motion of gravitational source can induce an additional centripetal force on the test particle, which may be comparable to or even larger than the conventional Newtonian gravitational force.     

Electrostatic self-force and material sources of the gravitational field

Using a multipolar expansion we determine the electrostatic potential generated by a point source held fixed in the Schwarzschild metric matched successively with two interior metrics, which describes, respectively, two forms of material distributions. The expression of the potential obtained is reformulated by means of the Copson-Linet potential, valid for the Schwarzschild black hole situation. The self-force acting on the source is then determined. We establish that its expression depends on the material sources of the gravitational field. The transition to the black hole situation is then performed.     

The Gravitational Waves from Test Particles around Black Holes Immersed in a Strong Magnetic Field

In this paper, we calculate the gravitational waveform from free test particles around Schwarzschild black holes immersed in a uniform strong magnetic field. By comparing with the cases of the Schwarzschild black holes, we find that for stable circle orbits, magnetic field can amplify amplitude and frequency of gravitational waves (here after GWs). For other general orbits, the uniform magnetic field also can amplify amplitude of GWs, enhance energy radiation of GWs and make it to shift to higher frequency. Another obvious influence of magnetic field B is that it can change the form of h _× component of GWs.     

Phase transition of quantum-corrected Schwarzschild black hole

We study the thermodynamic phase transition of a quantum-corrected Schwarzschild black hole. The modified metric affects the critical temperature which is slightly less than the conventional one. The space without black holes is not the hot flat space but the hot curved space due to vacuum fluctuations so that there appears a type of Gross–Perry–Yaffe phase transition even for the very small size of black hole, which is impossible for the thermodynamics of the conventional Schwarzschild black hole. We discuss physical consequences of the new phase transition in this framework.     

On gravitational shock waves in curved spacetimes

Some years ago Dray and 't Hooft found the necessary and sufficient conditions to introduce a gravitational shock wave in a particular class of vacuum solutions to Einstein's equations. We extend this work to cover cases where non-vanishing matter fields and a cosmological constant are present. The sources of gravitational waves are massless particles moving along a null surface such as a horizon in the case of black holes. After we discuss the general case we give many explicit examples. Among them are the d-dimensional charged black hole (that includes the 4-dimensional Reissner-Nordström and the d-dimensional Schwarzschild solution as subcases), the 4-dimensional De Sitter and anti-De Sitter spaces (and the Schwarzschild-De Sitter black hole), the 3-dimensional anti-De Sitter black hole, as well as backgrounds with a covariantly constant null Killing vector. We also address the analogous problem for string-inspired gravitational solutions nd give a few examples.     

The effects of running gravitational coupling on rotating black holes

In this work we investigate the consequences of running gravitational coupling on the properties of rotating black holes. Apart from the changes induced in the space-time structure of such black holes, we also study the implications to Penrose process and geodetic precession. We are motivated by the functional form of gravitational coupling previously investigated in the context of infra-red limit of asymptotic safe gravity theory. In this approach, the involvement of a new parameter \({\tilde{\xi }}\) in this solution makes it different from Schwarzschild black hole. The Killing horizon, event horizon and singularity of the computed metric is then discussed. It is noticed that the ergosphere is increased as \({\tilde{\xi }}\) increases. Considering the black hole solution in equatorial plane, the geodesics of particles, both null and time like cases, are explored. The effective potential is computed and graphically analyzed for different values of parameter \({\tilde{\xi }}\). The energy extraction from black hole is investigated via Penrose process. For the same values of spin parameter, the numerical results suggest that the efficiency of Penrose process is greater in quantum corrected gravity than in Kerr Black Hole. At the end, a brief discussion on Lense–Thirring frequency is also done.     

Ultrarelativistic black-hole encounters

A method is given for investigating the ultrarelativistic encounter of two black holes which complements the usual low-speed approximation. It depends on the fact that the ultrarelativistic limit of a moving Schwarzschild black hole is a certain plane-fronted impulsive gravitational wave. This enables linearized theory on a curved background to be used. The solution is obtained, with the help of generalized function techniques, to the first order in the background energy, and the radiation pattern at conformal null infinity is examined. The whole approach has a strong connection with the theory of twistors.     

Strong lensing of a regular black hole with an electrodynamics source

In this paper we have investigated the gravitational lensing phenomenon in the strong field regime for a regular, charged, static black holes with non-linear electrodynamics source. We have obtained the angle of deflection and compared it to a Schwarzschild black hole and Reissner Nordström black hole with similar properties. We have also done a graphical study of the relativistic image positions and magnifications. We hope that this method may be useful in the detection of non-luminous bodies like this current black hole.     

Energy spectrum of the Klein-Gordon equation in Schwarzschild and Kerr fields

We examine the influence of relativistic gravitational effects and rotation of a central body on the structure of the quasidiscrete energy spectrum of a spinless particle in the field of Schwarzschild and Kerr black holes.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 10, pp 71–76, October, 1988.