Evolution of the interior of a charged black hole

The Reissner-Nordström-Vaidya metric is used to study the classical instability of the inner (Cauchy) horizon in the Reissner-Nordström black hole interior. The back-reaction of the geometry to the instability turns the Cauchy horizon into an intermediate curvature singularity (or “whimper”) restoring predictability to the interior.     

Entropy bound of horizons for accelerating,rotating and charged Plebanski–Demianski black hole

We first review the accelerating, rotating and charged Plebanski–Demianski (PD) black hole, which includes the Kerr–Newman rotating black hole and the Taub-NUT spacetime. The main feature of this black hole is that it has 4 horizons like event horizon, Cauchy horizon and two accelerating horizons. In the non-extremal case, the surface area, entropy, surface gravity, temperature, angular velocity, Komar energy and irreducible mass on the event horizon and Cauchy horizon are presented for PD black hole. The entropy product, temperature product, Komar energy product and irreducible mass product have been found for event horizon and Cauchy horizon. Also their sums are found for both horizons. All these relations are dependent on the mass of the PD black hole and other parameters. So all the products are not universal for PD black hole. The entropy and area bounds for two horizons have been investigated. Also we found the Christodoulou–Ruffini mass for extremal PD black hole. Finally, using first law of thermodynamics, we also found the Smarr relation for PD black hole.     

Black hole evaporation in a noncommutative charged Vaidya model

We study the black hole evaporation and Hawking radiation for a noncommutative charged Vaidya black hole. For this purpose, we determine a spherically symmetric charged Vaidya model and then formulate a noncommutative Reissner-Nordstr?m-like solution of this model, which leads to an exact (t ? r)-dependent metric. The behavior of the temporal component of this metric and the corresponding Hawking temperature are investigated. The results are shown in the form of graphs. Further, we examine the tunneling process of charged massive particles through the quantum horizon. We find that the tunneling amplitude is modified due to noncommutativity. Also, it turns out that the black hole evaporates completely in the limits of large time and horizon radius. The effect of charge is to reduce the temperature from a maximum value to zero. We note that the final stage of black hole evaporation is a naked singularity.     

Singularities of noncompact charged objects

We formulate a model of noncompact spherical charged objects in the framework of noncommutative field theory. The Einstein-Maxwell field equations are solved with charged anisotropic fluid. We choose matter and charge densities as functions of two parameters instead of defining these quantities in terms of Gaussian distribution function. It is found that the corresponding densities and the Ricci scalar are singular at origin, whereas the metric is nonsingular, indicating a spacelike singularity. The numerical solution of the horizon equation implies that there are two or one or no horizon(s) depending on the mass. We also evaluate the Hawking temperature, and find that a black hole with two horizons is evaporated to an extremal black hole with one horizon.     

Black hole emissions and phase transitions

The nonthermal emission of a rotating black hole is related to the inner horizon of the hole. The transition from the Kerr black hole state to the naked singularity state is considered as a phase transition. An arrangement of the energetics of Kerr black holes into a two-phase thermodynamics is suggested.     

A boosted Kerr black hole solution and the structure of a general astrophysical black hole

A solution of Einstein’s vacuum field equations that describes a boosted Kerr black hole relative to an asymptotic Lorentz frame at future null infinity is derived. The solution has three parameters (mass, rotation and boost) and corresponds to the most general configuration that an astrophysical black hole must have; it reduces to the Kerr solution when the boost parameter is zero. In this solution the ergosphere is north-south asymmetric, with dominant lobes in the direction opposite to the boost. However the event horizon, the Cauchy horizon and the ring singularity—which are the core of the black hole structure—do not alter, being independent of the boost parameter. Possible consequences for astrophysical processes connected with Penrose processes in the asymmetric ergosphere are discussed.     

Quantum electron levels in the field of a charged black hole

Stationary solutions of the Dirac equation in the metric of the charged Reissner–Nordstrom black hole are found. In the case of an extremal black hole, the normalization integral of the wave functions is finite, and the regular stationary solution is physically self-consistent. The presence of quantum electron levels under the Cauchy horizon can have an impact on the final stage of the Hawking evaporation of the black hole, as well as on the particle scattering in the field of the black hole.     

Pulsation of black holes

The Hawking–Penrose singularity theorem states that a singularity forms inside a black hole in general relativity. To remove this singularity one must resort to a more fundamental theory. Using a corrected dynamical equation arising in loop quantum cosmology and braneworld models, we study the gravitational collapse of a perfect fluid sphere with a rather general equation of state. In the frame of an observer comoving with this fluid, the sphere pulsates between a maximum and a minimum size, avoiding the singularity. The exterior geometry is also constructed. There are usually an outer and an inner apparent horizon, resembling the Reissner–Nordström situation. For a distant observer the horizon crossing occurs in an infinite time and the pulsations of the black hole quantum “beating heart” are completely unobservable. However, it may be observable if the black hole is not spherical symmetric and radiates gravitational wave due to the quadrupole moment, if any.     

Charged Dirac Particles’ Hawking Radiation via Tunneling of Both Horizons and Thermodynamics Properties of Kerr–Newman–Kasuya–Taub–NUT–AdS Black Holes

We investigate Hawking radiation of electrically and magnetically charged Dirac particles from a dyonic Kerr–Newman–Kasuya–Taub–NUT–Anti-de Sitter (KNKTN–AdS) black hole by considering thermal characters of both the outer and inner horizons. We apply Damour–Ruffini method and membrane method to calculate the temperature and the entropy of the inner horizon of the KNKTN–AdS black hole. The inner horizon admits thermal character with positive temperature and entropy proportional to its area. The inner horizon entropy contributes to the total entropy of the black hole in the context of Nernst theorem. Considering conservation of energy, charges, angular momentum, and the back-reaction of emitting particles to the spacetime, we obtain the emission spectra for both the inner and outer horizons. The total emission rate is obtained as the product of the emission rates of the inner and outer horizons. It deviates from the purely thermal spectrum with the leading term exactly the Boltzman factor and can bring some information out. The result thus can be treated as an explanation to the information loss paradox.     

Motion and collision of particles near Plebanski-Demianski black hole: Shadow and gravitational lensing

Here we consider accelerating and rotating charged Plebanski-Demianski (PD) class of black hole metric as a particle accelerator. We obtain the geodesic motions (timelike, null and spacelike) of particles in a non-equatorial plane around the PD black hole. We find the effective potential, energy, angular momentum, impact parameters, and discuss the circular orbit. We study the center of mass energy of two neutral particles falling from infinity to near the non-extremal horizons (event and Cauchy horizons), extremal horizon, accelerating horizons, and near the center of the PD black hole. Also, we study the collision of a particle and a massless photon. Then we find the center of mass energy due to the collision of two massless photons in the PD black hole background. We compute the redshift and blueshift of the emitted photons by massive particles while light signal travels along null geodesics towards the observer located far away from the source. We study the Penrose process, which occurs within the ergosphere, and examines the particle’s motion with its implications. Here, we analyze the PD black hole shadow’s apparent shape, which forms far away from the black hole. We study the possible visibility of the PD black hole through photon’s shadow and energy emission rate. We also investigate the effect on the shadow of the PD black hole in plasma for a distant observer. We study the strong gravitational lensing by PD black hole. Finally, we analyze the deflection angle, lens equation, position, magnification, Einstein ring and observables by taking the supermassive PD black hole in the Galaxy’s center.     

Stationary solutions of the Dirac equation in the gravitational field of a charged black hole

A stationary solution of the Dirac equation in the metric of a Reissner-Nordström black hole has been found. Only one stationary regular state outside the black hole event horizon and only one stationary regular state below the Cauchy horizon are shown to exist. The normalization integral of the wave functions diverges on both horizons if the black hole is non-extremal. This means that the solution found can be only the asymptotic limit of a nonstationary solution. In contrast, in the case of an extremal black hole, the normalization integral is finite and the stationary regular solution is physically self-consistent. The existence of quantum levels below the Cauchy horizon can affect the final stage of Hawking black hole evaporation and opens up the fundamental possibility of investigating the internal structure of black holes using quantum tunneling between external and internal states.     

Overcharging a Reissner-Nordstr?m Taub-NUT regular black hole

The destruction of a regular black hole event horizon might provide us the possibility to access regions inside black hole event horizon. This paper investigates the possibility of overcharging a charged Taub-NUT regular black hole via the scattering of a charged field and the absorption of a charged particle. For the charged scalar field scattering, both the near-extremal and extremal charged Taub-NUT regular black holes cannot be overcharged. For the test charged particle absorption, the result shows that the event horizon of the extremal charged Taub-NUT regular black hole still exists while the event horizon of the near-extremal one can be destroyed. However, if the charge and energy cross the event horizon in a continuous path, the near-extremal charged Taub-NUT regular black hole might not be overcharged.     

Spin Entropy for Kerr Black Holes

It is known that the entropy for a singular spacetime metric can be calculated in the framework of classical field theories by applying Noether's theorem to stationary solutions of Einstein's field equations, integrating a suitable form on a trapping surface for the singularity. When the Kerr solution is considered, two different horizons appear. The physical entropy for the system is well known to be related to the outer horizon. We investigate here which is the meaning of the entropy calculated (via first principle of black hole thermodynamics) on the inner horizon. We show that this entropy, which was earlier interpreted as a sort of "spin entropy" of the black hole, admits in fact an interpretation as a quantity associated to a conserved charge which is related to the rotational degrees of freedom of the system.     

On the Rigidity Theorem for Spacetimes with a Stationary Event Horizon or a Compact Cauchy Horizon

We consider smooth electrovac spacetimes which represent either (A) an asymptotically flat, stationary black hole or (B) a cosmological spacetime with a compact Cauchy horizon ruled by closed null geodesics. The black hole event horizon or, respectively, the compact Cauchy horizon of these spacetimes is assumed to be a smooth null hypersurface which is non-degenerate in the sense that its null geodesic generators are geodesically incomplete in one direction. In both cases, it is shown that there exists a Killing vector field in a one-sided neighborhood of the horizon which is normal to the horizon. We thereby generalize theorems of Hawking (for case (A)) and Isenberg and Moncrief (for case (B)) to the non-analytic case. Received: 4 November 1998 / Accepted: 13 February 1999     

Singularity Avoidance of Charged Black Holes in Loop Quantum Gravity

Based on spherically symmetric reduction of loop quantum gravity, quantization of the portion interior to the horizon of a Reissner-Nordström black hole is studied. Classical phase space variables of all regions of such a black hole are calculated for the physical case M ²>Q ². This calculation suggests a candidate for a classically unbounded function of which all divergent components of the curvature scalar are composed. The corresponding quantum operator is constructed and is shown explicitly to possess a bounded operator. Comparison of the obtained result with the one for the Schwarzschild case shows that the upper bound of the curvature operator of a charged black hole reduces to that of Schwarzschild at the limit Q→0. This local avoidance of singularity together with non-singular evolution equation indicates the role quantum geometry can play in treating classical singularity of such black holes.     

Acceleration of particles in Einstein-Maxwell-dilaton black holes

It has recently been pointed out that, under certain conditions, the energy of particles accelerated by black holes in the center-of-mass frame can become arbitrarily high. In this paper, we study the collision of two particles in the case of four-dimensional charged nonrotating, extremal charged rotating and near-extremal charged rotating Kaluza-Klein black holes as well as the naked singularity case in Einstein-Maxwell-dilaton theory. We find that the center-of-mass energy for a pair of colliding particles is unlimited at the horizon of charged nonrotating Kaluza-Klein black holes, extremal charged rotating Kaluza-Klein black holes and in the naked singularity case.     

Tunneling Effect of Two Horizons from a Reissner-Nordstrom Black Hole

The understanding of possible role played by the inner horizon of black holes in black hole thermodynamics is still somewhat incomplete. By adopting Damour-Ruffini method and the thin film model which is developed on the base of brick wall model suggested by ’t Hooft, we calculate the temperature and the entropy of the inner horizon of a R-N black hole. We conclude that the temperature of inner horizon is positive and the entropy of the inner horizon is proportional to the area of the inner horizon. In addition, the cut-off factor is 90β, which is same in calculation of the entropy of the outer horizon. So, we prove the existence of thermal characters of the inner horizon. Then, we discuss that if the contribution of the inner horizon is taken into account to the total entropy of the black hole, the Nernst theorem can be satisfied. At last, we study the tunneling effect including the inner horizon of the Reissner-Nordstrom black hole. We calculate the tunneling rate of the outer horizon Γ₊ and the inner horizon Γ₋. The total tunneling rate Γ should be the product of the rates of the outer and inner horizon, Γ=Γ₊⋅Γ₋. We find that the total tunneling rate is in agreement with the Parikh’s standard result, Γ→exp (ΔS _BH ), and there is no information loss.     

Vaidya-Bonner-de Sitter时空中荷电Dirac粒子的Hawking辐射

在Vaidya-Bonner-de Siter时空中，准确地给出了黑洞内外视界及宇宙视界的位置，研究了该时空中黑洞外视界和宇宙视界附近荷电Dirac粒子的Hawking辐射，确定三个视界面中任何两个都不可能重合． 关键词：     

$$$$-Dimensional charged black holes with scalar hair in Einstein–Power–Maxwell Theory

In \((2+1)\)-dimensional AdS spacetime, we obtain new exact black hole solutions, including two different models (power parameter \(k=1\) and \(k\ne 1\)), in the Einstein–Power–Maxwell (EPM) theory with nonminimally coupled scalar field. For the charged hairy black hole with \(k\ne 1\), we find that the solution contains a curvature singularity at the origin and is nonconformally flat. The horizon structures are identified, which indicates the physically acceptable lower bound of mass in according to the existence of black hole solutions. Later, the null geodesic equations for photon around this charged hairy black hole are also discussed in detail.     

Perturbative Approach to the Inner Structure of a Rotating Black Hole

This is the first in a series of papers analyzing the inner structure of a generic rotating black hole. The black hole is assumed to evolve from the gravitational collapse of an isolated rotating object in an empty asymptotically-flat universe. This paper covers the first stages of the evolution: from the gravitational collapse and the formation of a black hole, up to the stage where the black hole settles down to Kerr. We shall discuss the generalization of Price's analysis (regarding the latetime asymptotic decay of perturbations outside the black hole) from Schwarzschild to Kerr, and present preliminary results. We then consider these external small perturbations as initial data for the evolution of perturbations inside the black hole. We demonstrate that an important region inside the black hole, which we call the late-time region (and which extends up to the inner horizon) experiences (arbitrarily) small initial perturbations. This, we argue, justifies the attempt to apply the small-perturbation approach to the black hole's interior. We discuss the physical significance of this late-time region. We shall also outline the strategy we use for evolving the perturbations from the event horizon to the inner horizon.