The Inner Structure of Black Holes

We study the gravitational collapse of a self-gravitating charged scalar-field. Starting with a regular spacetime, we follow the evolution through the formation of an apparent horizon, a Cauchy horizon and a final central singularity. We find a null, weak, mass-inflation singularity along the Cauchy horizon, which is a precursor of a strong, spacelike singularity along the r = 0 hypersurface. The inner black hole region is bounded (in the future) by singularities. This resembles the classical inner structure of a Schwarzschild black hole and it is remarkably different from the inner structure of a charged static Reissner-Nordström or a stationary rotating Kerr black holes.     

利用广义不确定关系计算 Reissner-Nordström-de Sitter黑洞的统计力学熵

利用广义不确定关系修正的态密度方程并采用Wentzel-Kramers-Brillouin (WKB) 近似方法, 计算了Reissner-Nordström-de Sitter (RNdS) 黑洞时空中标量场的统计力学熵. 结果表明, 由这种方法得到的黑洞熵与它的内、外视界面积和宇宙视界面积之和成正比, 这与采用其他方法所得的结果一致, 从而揭示了黑洞熵与视界面积之间的内在联系, 也进一步表明了黑洞熵是视界面上量子态的熵, 是一种量子效应.     

Null geodesics in black hole metrics with non-zero cosmological constant

We study the radial motion along null geodesics in the Reissner-Nordström-de Sitter and Kerr-de Sitter space-times. We analyze the properties of the effective potential and we discuss circular orbits. We find that:

Holographic superconductor in the analytic hairy black hole

We study the charged black hole of hyperbolic horizon with scalar hair (charged Martinez-Troncoso-Zanelli: CMTZ black hole) as a model of analytic hairy black hole for holographic superconductor. For this purpose, we investigate the second order phase transition between CMTZ and hyperbolic Reissner-Nordström-AdS (HRNAdS) black holes. However, this transition unlikely occurs. As an analytic treatment for holographic superconductor, we develop superconductor in the bulk and superfluidity on the boundary using the CMTZ black hole below the critical temperature. The presence of charge destroys the condensates around the zero temperature, which is in accord with the thermodynamic analysis of the CMTZ black hole.     

Entropy of Reissner–Nordström–anti-de Sitter Black Hole

By using the method of quantum statistics, we directly derive the partition function of bosonic and fermionic field in Reissner-Nordström-anti-de Sitter black hole and obtain the integral expression of black hole's entropy. It avoids the difficulty in solving the wave equation of various particles. Then via the improved brick-wall method, membrane model, we calculate the statistical entropy of a film with the thickness of (N – 1) around the outside of horizon. In our result we can choose proper parameter in order to let the thickness of film tend to zero and have it approach the surface of horizon. Consequently, the entropy of black hole is proportional to the area of horizon. The stripped term and the divergent logarithmic term in the original brick-wall method no longer exist. In the whole process, physics idea is clear; calculation is simple. We offer a new simple and direct way of calculating the entropy of different complicated black holes.     

Generalized uncertainty principle, modified dispersion relation and Reissner-Nordström black hole tunneling radiation

The Parikh-Kraus-Wilczek tunneling proposal of black hole tunneling radiation is considered. Reissner-Nordström black hole thermodynamics is studied according to the generalized uncertainty principle and the modified dispersion relation analysis. It is shown that entropy, temperature and the original Parikh-Kraus-Wilczek calculation of the black hole tunneling probability receive new corrections. The results of these two alternative approaches are identical if one uses the suitable expansion coefficients.     

Spacetime Embedding Diagrams for Spherically Symmetric Black Holes

We show that it is possible to embed the 1 + 1 dimensional reduction of certain spherically symmetric black hole spacetimes into 2 + 1 Minkowski space. The spacetimes of interest (Schwarzschild de-Sitter, Schwarzschild anti de-Sitter, and Reissner-Nordström near the outer horizon) represent a class of metrics whose geometries allow for such embeddings. The embedding diagrams have a dynamic character which allows one to represent the motion of test particles. We also analyze various features of the embedding construction, deriving the general conditions under which our procedure provides a smooth embedding. These conditions also yield an embedding constant related to the surface gravity of the relevant horizon.     

Are all static black hole solutions spherically symmetric?

The static black hole solutions to the Einstein-Maxwell equations are all spherically symmetric, as are many of the recently discovered black hole solutions in theories of gravity coupled to other forms of matter. However, counterexamples demonstrating that static black holes need not be spherically symmetric exist in theories, such as the standard electroweak model, with electrically charged massive vector fields. In such theories, a magnetically charged Reissner-Nordström solution with sufficiently small horizon radius is unstable against the development of a nonzero vector field outside the horizon. General arguments show that, for generic values of the magnetic charge, this field cannot be spherically symmetric. Explicit construction of the solution shows that it in fact has no rotational symmetry at all.This essay received the second award from the Gravity Research Foundation, 1995-Ed.     

Domain wall universe in the Einstein–Born–Infeld theory

In this Letter, we discuss the dynamics of a domain wall universe embedded into the charged black hole spacetime of the Einstein–Born–Infeld (EBI) theory. There are four kinds of possible spacetime structures, i.e., those with no horizon, the extremal one, those with two horizons (as the Reissner–Nordström black hole), and those with a single horizon (as the Schwarzshild black hole). We derive the effective cosmological equations on the wall. In contrast to the previous works, we take the contribution of the electrostatic energy on the wall into account. By examining the properties of the effective potential, we find that a bounce can always happen outside the (outer) horizon. For larger masses of the black hole, the height of the barrier between the horizon and bouncing point in the effective potential becomes smaller, leading to longer time scales of bouncing process. These results are compared with those in the previous works.     

Letter: Quasinormal Modes of the Electrically Charged Dilaton Black Hole

We sketch the results of calculations of the quasinormal frequencies of the electrically charged dilaton black hole. At the earlier phase of evaporation (Q is less than 0.7–0.8M), the dilaton black hole rings with the complex frequencies which differ negligibly from those of the Reissner-Nordström black hole. The spectrum of the frequencies weakly depends upon the dilaton coupling.     

Entropy is conserved in Hawking radiation as tunneling: A revisit of the black hole information loss paradox

We revisit in detail the paradox of black hole information loss due to Hawking radiation as tunneling. We compute the amount of information encoded in correlations among Hawking radiations for a variety of black holes, including the Schwarzchild black hole, the Reissner–Nordström black hole, the Kerr black hole, and the Kerr–Newman black hole. The special case of tunneling through a quantum horizon is also considered. Within a phenomenological treatment based on the accepted emission probability spectrum from a black hole, we find that information is leaked out hidden in the correlations of Hawking radiation. The recovery of this previously unaccounted for information helps to conserve the total entropy of a system composed of a black hole plus its radiations. We thus conclude, irrespective of the microscopic picture for black hole collapsing, the associated radiation process: Hawking radiation as tunneling, is consistent with unitarity as required by quantum mechanics.     

Wave function of the quantum black hole

We show that the Wald Noether-charge entropy is canonically conjugate to the opening angle at the horizon. Using this canonical relation, we extend the Wheeler–DeWitt equation to a Schrödinger equation in the opening angle, following Carlip and Teitelboim. We solve the equation in the semiclassical approximation by using the correspondence principle and find that the solutions are minimal uncertainty wavefunctions with a continuous spectrum for the entropy and therefore also of the area of the black hole horizon. The fact that the opening angle fluctuates away from its classical value of 2π indicates that the quantum black hole is a superposition of horizonless states. The classical geometry with a horizon serves only to evaluate quantum expectation values in the strict classical limit.     

Entropy of higher-dimensional charged Gauss–Bonnet black hole in de Sitter space

The fundamental equation of the thermodynamic system gives the relation between the internal energy, entropy and volume of two adjacent equilibrium states. Taking a higher-dimensional charged Gauss–Bonnet black hole in de Sitter space as a thermodynamic system, the state parameters have to meet the fundamental equation of thermodynamics. We introduce the effective thermodynamic quantities to describe the black hole in de Sitter space. Considering that in the lukewarm case the temperature of the black hole horizon is equal to that of the cosmological horizon, we conjecture that the effective temperature has the same value. In this way, we can obtain the entropy formula of spacetime by solving the differential equation. We find that the total entropy contains an extra term besides the sum of the entropies of the two horizons. The corrected term of the entropy is a function of the ratio of the black hole horizon radius to the cosmological horizon radius, and is independent of the charge of the spacetime.     

QUASILOCAL ENERGY FOR STATIONARY AXISYMMETRIC EMDA BLACK HOLE

By using Brown-York quasilocal energy theory we calculate the quasilocal energy of a stationary axisymmetic EMDA black hole and explore the universality of Martinez's conjecture in string theory. We show that the energy is positive and monotonically decreases to the ADM mass at spatial infinity, and the Martinez's conjecture, the Brown-York quasilocal energy at the outer horizon reduces to twice its irreducible mass, is still valid for stationary axisymmetric EMDA black hole. From the result we also find that the Kerr-Sen spacetime keeps up with Martinez's conjecture. This is different from the Bose-Naing result that the quasilocal energy of the Kerr-Sen spacetime does not approach the Martinez's conjecture.     

The real scalar field in extreme RNdS space

The real scalar field equation between the outer black hole horizon and the cosmological horizon is solved in the extreme Reissner-Nordström de Sitter (RNdS) space. We use an accurate approximation, the polynomial approximation, to approximate the tortoise coordinate x(r) in order to get the inverse function r = r(x) and then to solve the wave equation. The case where the two horizons are very close to each other is discussed in detail. We find that the wave function is harmonic only in the very small regions near the horizons, and the amplitude decreases remarkably near the potential peak because of the effect of the potential. Furthermore, it is found that the height of the potential increases as the cosmological constant Λ decreases, and the wave amplitude will decrease more remarkably with less Λ.     

Globally regular solutions of a schwarzschild black hole and a Reissner-Nordström black hole

A new physical concept about globally regular solutions is suggested. The globally regular solutions corresponding to the Schwarzschild black hole and the Reissner-Nordström black hole are examined.     

直线加速运动动态黑洞的熵

选取超前爱丁顿坐标,采用薄膜brickwall模型,计算Kinnersley度规表述的直线加速运动动态黑洞的熵.通过此方法,可以给出视界面上每一点的温度和熵密度.这一结果表明,熵与视界面积成正比的结论,不仅适用于整个视界,也适用于视界面上的局部;不仅适用于稳态黑洞,也适用于动态黑洞.在薄膜趋于视界面时,其厚度也趋于零,薄膜本身成为视界面,黑洞熵就是视界面上量子态的熵 关键词： 熵 加速黑洞 薄膜brickwall模型     

Energy, momentum and angular momentum in the dyadosphere of a charged spacetime in teleparallel equivalent of general relativity

We apply the energy momentum and angular momentum tensor to a tetrad field, with two unknown functions of radial coordinate, in the framework of a teleparallel equivalent of general relativity (TEGR). The definition of the gravitational energy is used to investigate the energy within the external event horizon of the dyadosphere region for the Reissner-Nordström black hole. We also calculate the spatial momentum and angular momentum.     

Generalized Uncertainty Principle and Correction Value to the Kerr Black Hole Entropy

Recently, there has been much attention devoted to resolving the quantum corrections to the Bekenstein-Hawking black hole entropy. In particular, many researchers have expressed a vested interest in the coefficient of the logarithmic term of the black hole entropy correction term. In this paper, we calculate the correction value of the black hole entropy by utilizing the generalized uncertainty principle and obtain the correction term caused by the generalized uncertainty principle. Because in our calculation we think that the Bekenstein-Hawking area theorem is still valid after considering the generalized uncertainty principle, we derive that the coefficient of the logarithmic term of the black hole entropy correction term is positive. This result is different from the known result at present. Our method is valid not only for single horizon spacetime but also for spin axial symmetric spacetimes with double horizons. In the whole process, the physics idea is clear and calculation is simple. It offers a new way for studying the entropy correction of the complicated spacetime.     

Asymptotically de Sitter and anti-de Sitter black holes with confining electric potential

We study gravity interacting with a special kind of QCD-inspired nonlinear gauge field system which earlier was shown to yield confinement-type effective potential (the “Cornell potential”) between charged fermions (“quarks”) in flat space-time. We find new static spherically symmetric solutions generalizing the usual Reissner-Nordström-de Sitter and Reissner-Nordström-anti-de Sitter black holes with the following additional properties: (i) appearance of a constant radial electric field (in addition to the Coulomb one); (ii) novel mechanism of dynamical generation of cosmological constant through the non-Maxwell gauge field dynamics; (iii) appearance of confining-type effective potential in charged test particle dynamics in the above black hole backgrounds.