Entropy Quantization of Schwarzschild Black Hole

The surface gravity of Schwarzschild black hole can be quantized from the test particle moving around different energy states analog to the Bohr's atomic model. We have quantized the Hawking temperature and entropy of Schwarzschild black hole from quantization of surface gravity. We also have shown that the change of entropy reduces to zero when the boundary shrinks to very small size.     

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.     

Second Order Perturbations of a Schwarzschild Black Hole: Inclusion of Odd Parity Perturbations

We consider perturbations of a Schwarzschild black hole that can be of both even and odd parity, keeping terms up to second order in perturbation theory, for the l = 2 axisymmetric case. We develop explicit formulae for the evolution equations and radiated energies and waveforms using the Regge–Wheeler–Zerilli approach. This formulation is useful, for instance, for the treatment in the "close limit approximation" of the collision of counterrotating black holes.     

The Exact Harmonic Metric for a Moving Reissner-Nordstrom Black Hole

The exact harmonic metric for a moving Reissner-Nordstr6m black hole with an arbitrarily constant speed is presented. As an application, the post-Newtonian dynamics of a non-relativistic particle in this field is calculated.     

Gravitational Deflection of Massive Particles by a Schwarzschild Black Hole in Radiation Gauge*

The exact metric of a Schwarzschild black hole in the true radiation gauge was recently reported.In this work, we base on this gravity and calculate the gravitational deflection of relativistic massive particles up to the fourth post-Minkowskian order. It is found that the result is consistent with the previous formulations for both the case of dropping the fourth-order contribution and the case of light deflection. Our result might be helpful for future high-accuracy observations.     

Entropy of a Uniformly Accelerating Black Hole

Kinnersley has discussed the space–time of an arbitrarily accelerating point mass. We select a simple case in which the black hole is uniformly accelerated and the mass does not vary with time. We adopt thin film brick-wall model to calculate the entropy of black hole. We find that both the temperature and the entropy density of black hole can be calculated at every point on the horizon. This result indicates that the conclusion that black hole entropy is proportional to its area can be applied to horizon not only globally, but also locally.     

From Schwarzschild to Kerr due to Black Hole Quantum Tunnelling

Hawking radiation can be viewed as a process of quantum tunnelling near black hole horizon. When a particle with angular momentum tunnels across the event horizon of Schwarzschild black hole, the black hole will change into a Kerr black hole. The emission rate of the massless particles with angular momentum is calculated, and the result is consistent with an underlying unitary theory.     

Quasinormal Modes of the Schwarzschild Black Hole Surrounded by the Quintessence Field in Rastall Gravity

The quasinormal modes of the Schwarzschild black hole surrounded by the quintessence in Rastall gravity are studied using the sixth-order Wentzel-Kramers-Brillouin approximative approach. The effect of the Rastall parameter on the quasinormal modes of gravitational, electromagnetic and massless scalar perturbations is explored. Compared to the case of Einstein gravity, it is found that, when η < 0, the gravitational field, electromagnetic field as well as massless scalar field damp more rapidly and have larger real frequency of oscillation in Rastall gravity, while when η > 0, the gravitational field, electromagnetic field as well as massless scalar field damp more slowly and have smaller real frequency of oscillation in Rastall gravity. It is also found that the gravitational field, electromagnetic field as well as massless scalar field damp more and more slowly and the real frequency of oscillation for the gravitational perturbation, electromagnetic perturbation as well as massless scalar perturbation becomes smaller and smaller as the Rastall parameter η increases. Compared among the quasinormal frequencies of gravitational, electromagnetic and massless scalar perturbations, I find that, for fixed η, (l, n), ∈ and N_q, the oscillation damps most slowly for the gravitational perturbation, mediate for the electromagnetic perturbation and most rapidly for the massless scalar perturbation, and the real frequency of oscillation is the smallest for the gravitational perturbation, mediate for the electromagnetic perturbation and the largest for the massless scalar perturbation in Rastall gravity.     

Falling into a Schwarzschild black hole

Consider a radially freely falling observer who plunges into a Schwarzschild black hole. In contrast to a static observer, he will have a different view of the black hole and of the outer sky. Furthermore, the relationship between the proper time of the falling observer and the proper time of a distant static observer differs from the relationship between the proper times of two static observers or two freely falling observers.     

Analytic observation of a star orbiting a Schwarzschild black hole

A star orbiting a Schwarzschild black hole can be used as a toy model for an educational study of the relativistic effects like bending of light, geodesic precession, and frequency shift. Additionally, the finiteness of the speed of light plays a crucial role for the visual appearance of the star. We will develop an analytic method to show the difference between the actual and the apparent position of the star depending on the observation time and the observer’s inclination to the orbital plane.     

Interior of a Schwarzschild Black Hole Revisited

The Schwarzschild solution has played a fundamental conceptual role in general relativity, and beyond, for instance, regarding event horizons, spacetime singularities and aspects of quantum field theory in curved spacetimes. However, one still encounters the existence of misconceptions and a certain ambiguity inherent in the Schwarzschild solution in the literature. By taking into account the point of view of an observer in the interior of the event horizon, one verifies that new conceptual difficulties arise. In this work, besides providing a very brief pedagogical review, we further analyze the interior Schwarzschild black hole solution. Firstly, by deducing the interior metric by considering time-dependent metric coefficients, the interior region is analyzed without the prejudices inherited from the exterior geometry. We also pay close attention to several respective cosmological interpretations, and briefly address some of the difficulties associated to spacetime singularities. Secondly, we deduce the conserved quantities of null and timelike geodesics, and discuss several particular cases in some detail. Thirdly, we examine the Eddington–Finkelstein and Kruskal coordinates directly from the interior solution. In concluding, it is important to emphasize that the interior structure of realistic black holes has not been satisfactorily determined, and is still open to considerable debate.     

Harrison Metrics for the Schwarzschild Black Hole

Based on the hidden conformed symmetry, some authors have proposed a Harrison metric for the Schwarzschild black hole. We give a procedure which can generate a family of Harrison metrics starting from a general set of SL（2, R） vector fields. By analogy with the subtracted geometry of the Kerr black hole, we find a new Harrison metric for the Schwaxzschild case. its conformal generators axe also investigated using the Killing equations in the near-horizon limit.     

CGHS Black Hole Analog Moving Mirror and Its Relativistic Quantum Information as Radiation Reaction

The Callan–Giddings–Harvey–Strominger black hole has a spectrum and temperature that correspond to an accelerated reflecting boundary condition in flat spacetime. The beta coefficients are identical to a moving mirror model, where the acceleration is exponential in laboratory time. The center of the black hole is modeled by the perfectly reflecting regularity condition that red-shifts the field modes, which is the source of the particle creation. In addition to computing the energy flux, we find the corresponding moving mirror parameter associated with the black hole mass and the cosmological constant in the gravitational analog system. Generalized to any mirror trajectory, we derive the self-force (Lorentz–Abraham–Dirac), consistently, expressing it and the Larmor power in connection with entanglement entropy, inviting an interpretation of acceleration radiation in terms of information flow. The mirror self-force and radiative power are applied to the particular CGHS black hole analog moving mirror, which reveals the physics of information at the horizon during asymptotic approach to thermal equilibrium.     

Parikh-Wilczek Tunneling as Massive Particles from Noncommutative Schwarzschild Black Hole

In this paper, we apply the tunneling of massive particle through the quantum horizon of a Schwarzschild black hole in noncommutative spaeetime. The tunneling effects lead to modified Hawking radiation due to inclusion of back-reaction effects. Our calculations show also that noncommutativity effects cause the further modifications to the thermodynamical relations in black hole. We calculate the emission rate of the massive particles＇ tunneling from a Schwarzschild black hole which is modified on account of noncommutativity influences. The issues of information loss and possible correlations between emitted particles are discussed. Unfortunately even by considering noneommutativity view point, there is no correlation between different modes of evaporation at least at late-time. Nevertheless, as a result of spacetime noncommutativity, information may be conserved by a stable black hole remnant.     

Parikh-Wilczek Tunneling as Massive Particles from Noncommutative Schwarzschild Black Hole

In this paper, we apply the tunneling of massive particle through the quantum horizon of a Schwarzschild black hole in noncommutative spacetime. The tunneling effects lead to modified Hawking radiation due to inclusion of back-reaction effects. Our calculations show also that noncommutativity effects cause the further modifications to the hermodynamical relations in black hole. We calculate the emission rate of the massive particles' tunneling from aSchwarzschild black hole which is modified on account of noncommutativity influences. The issues of information loss and possible correlations between emitted particles are discussed. Unfortunately even by considering noncommutativity view point, there is no correlation between different modes of evaporation at least at late-time. Nevertheless, as a result of spacetime noncommutativity, information may be conserved by a stable black hole remnant.     

Quantum Kinetic Theory of a Massless Scalar Model in the Presence of a Schwarzschild Black Hole

We employ quantum kinetic theory to investigate local quantum physics in the background of spherically symmetric and neutral black holes formed through the gravitational collapse. For this purpose in mind, we derive and study the covariant Wigner distribution function near to and far away from the black‐hole horizon. We find that the local density of the particle number is negative in the near‐horizon region, while the entropy density is imaginary. These pose a question whether kinetic theory is applicable in the near‐horizon region. We elaborate on that and propose a possible interpretation of how this result might nevertheless be self‐consistently understood.     

Casimir Energy for Spherical Shell in Schwarzschild Black Hole Background

In this paper, we consider the Casimir energy of massless scalar fields which satisfy the Dirichlet boundary condition on a spherical shell. Outside the shell, the spacetime is assumed to be described by the Schwarzschild metric, while inside the shell it is taken to be the flat Minkowski space. Using zeta function regularization and heat kernel coefficients we isolate the divergent contributions of the Casimir energy inside and outside the shell, then using the renormalization procedure of the bag model the divergent parts are cancelled, finally obtaining a renormalized expression for the total Casimir energy.     

Hawking Temperature of a Static Black Hole in Harmonic Coordinates

Hawking radiation is usually studied in standard coordinates. In this paper, we calculate the Hawking temperature of a Schwarzschild black hole in harmonic coordinates, as well as that of a Reissner-Nordström black hole. The action of a scalar field near the event horizon can be formulated exactly without omitting some high-order terms. We show dimensional reduction for Hawking temperature is also valid for harmonic coordinates, and verify further that the results are independent on concrete coordinates. With the help of Lorentz transformation, our work might also serve as a basis to investigate the thermal radiation from a moving black hole.     

Covariant Anomaly and Hawking Radiation from Kerr-Newman Black Hole in Dragging Coordinates Frame

in the light of Robinson and Wilczek＇s new idea, and motivated by Banerjee and Kulkarni＇s simplified method of using only the covariant anomaly to derive Hawking radiation from a black hole, we generally extend the work to Kerr-Newman black hole in dragging coordinates frame. It is shown that the flows introduced to cancel the anomaly at the event horizon are equal to the corresponding Hawking radiation in dragging coordinates frame, which supports and extends Robinson and Wilczek＇s opinion.