RN Black Hole Research Articles

Understanding first law of thermodynamics of black holes

We approach the thermodynamic properties of the d-dimensional RN black holes, discuss the three expressions for the first law of thermodynamics for black holes and calculate the energies in the three regions of the black hole spacetimes. Some remarks of the first law of thermodynamics and the thermal properties for the black holes are given.

ABSORPTION CROSS SECTION OF A RN BLACK HOLE

The behavior of a charged scalar field in the RN black hole space–time is studied using the WKB approximation. In the present work, it is assumed that matter waves can be reflected from the event horizon. Using this effect, the Hawking temperature and the absorption cross section for an RN black hole placed in a charged scalar field are calculated. The absorption cross section σabs is found to be inversely proportional to the square of the Hawking temperature of the black hole.

THERMODYNAMIC GEOMETRY AND CRITICAL BEHAVIOR OF BLACK HOLES

Based on the observations that there exists an analogy between the Reissner–Nordström–Anti-de Sitter (RN–AdS) black holes and the van der Waals–Maxwell liquid-gas system, in which a correspondence of variables is (ϕ,q) ↔ (V,P), we study the Ruppeiner geometry, defined as Hessian matrix of black hole entropy with respect to the internal energy (not the mass) of black hole and electric potential (angular velocity), for the RN, Kerr and RN–AdS black holes. It is found that the geometry is curved and the scalar curvature goes to negative infinity at the Davies' phase transition point for the RN and Kerr black holes. Our result for the RN–AdS black holes is also in good agreement with the one about phase transition and its critical behavior in the literature.

Energy distribution in Reissner–Nordström anti-de Sitter black holes in the Møller prescription

The energy (due to matter plus fields including gravity) distribution of the Reissner–Nordstrom anti-de Sitter (RN AdS) black holes is studied by using the Moller energy-momentum definition in general relativity. This result is compared with the energy expression obtained by using the Einstein and Tolman complexes. The total energy depends on the black hole mass M and charge Q and the cosmological constant Λ. The energy distribution of the RN AdS is also calculated by using the Moller prescription in teleparallel gravity. We get the same result for both of these different gravitation theories. The energy obtained is also independent of the teleparallel dimensionless coupling constant, which means that it is valid not only in the teleparallel equivalent of general relativity, but also in any teleparallel model. In special cases of our model, we also discuss the energy distributions associated with the Schwarzschild AdS, RN and Schwarzschild black holes, respectively.

Geometry of higher-dimensional black hole thermodynamics

We investigate thermodynamic curvatures of the Kerr and Reissner-Nordstr\"om (RN) black holes in spacetime dimensions higher than four. These black holes possess thermodynamic geometries similar to those in four dimensional spacetime. The thermodynamic geometries are the Ruppeiner geometry and the conformally related Weinhold geometry. The Ruppeiner geometry for $d=5$ Kerr black hole is curved and divergent in the extremal limit. For $d \geq 6$ Kerr black hole there is no extremality but the Ruppeiner curvature diverges where one suspects that the black hole becomes unstable. The Weinhold geometry of the Kerr black hole in arbitrary dimension is a flat geometry. For RN black hole the Ruppeiner geometry is flat in all spacetime dimensions, whereas its Weinhold geometry is curved. In $d \geq 5$ the Kerr black hole can possess more than one angular momentum. Finally we discuss the Ruppeiner geometry for the Kerr black hole in $d=5$ with double angular momenta.

Quasinormal modes for Weyl neutrino field in RN black holes

We employ the WKB approximation up to the third order to determine the low-lying quasinormal modes for the Weyl neutrino field in RN black holes, which are the most relevant to the evolution of the field around a black hole in the intermediate stage. It is shown that the quasinormal mode frequencies for the Weyl neutrino field in RN black holes are different from those in Schwarzschild black holes owing to the charge-induced additional gravitation, and the variations of the quasinormal mode frequencies for the Weyl neutrino field are similar to those for integral spin fields in RN black holes.

Decay of a charged scalar field around a black hole: Quasinormal modes of RN, RNAdS, and dilaton black holes

It is well known that the charged scalar perturbations of the Reissner-Nordstr\"om metric will decay slower at very late times than the neutral ones, thereby dominating in the late time signal. We show that, at the stage of quasinormal (QN) ringing, on the contrary, the neutral perturbations will decay slower for RN, RNAdS and dilaton black holes. The QN frequencies of the nearly extreme RN black hole have the same imaginary parts (damping times) for charged and neutral perturbations. An explanation of this fact is not clear but, possibly, is connected with the Choptuik scaling.

Inner Structure of Entropy of Reissner–Nordström Black Holes

Using the relationship between the entropy and the Euler characteristic, and the usual decomposition of spin connection, an entropy density is introduced to describe the inner structure of the entropy of RN black holes. It is pointed out that the entropy of RN black holes is determined by the singularities of the timelike Killing vector field of RN spacetime, and that these singularities carry the topological numbers, Hopf indices and Brouwer degrees, naturally, which are topological invariants. Taking account of the physical meaning of entropy in statistics, the entropy and its density of RN black holes are modified and they are given by the Hopf indices merely.

Back reaction on a Reissner-Nordström black hole

The perturbed (``dressed'') metric of the conformally invariant scalar field in a Reissner-Nordstr\"om (RN) black hole is given by solving the semiclassical Einstein and Maxwell equations according to York's back-reaction approach. Some properties of the ``dressed'' black hole are obtained, such as its ``dressed'' mass, the location of the event horizon, and its surface gravity. It will also be found that the hypersurfaces of ${r}_{+}$ and ${r}_{\ensuremath{-}},$ which are the event and Cauchy horizons in the ``naked'' RN black hole, become spacelike in the perturbed geometry.

Massive Dirac fields in naked and in black hole Reissner-Nordström manifolds

The problem of the electrodynamical stability of the RN naked singularities is analyzed by studying the qualitative spectral properties of the Dirac equation. A comparison with the RN black hole cases is made. The Dirac vacuum appears to be stable in the case of the naked RN geometries, whereas in the case of the RN black holes the same mathematical approach confirms the existence of a discharge mechanism related with the Klein effect.

Charged black holes in quadratic theories.

We point out that in general the Reissner-Nordstr\"om (RN) charged black holes of general relativity are not solutions of the four dimensional quadratic gravitational theories. They are, e.g., exact solutions of the $R+R^2$ quadratic theory but not of a theory where a $R_{ab}R^{ab}$ term is present in the gravitational Lagrangian. In the case where such a non linear curvature term is present with sufficiently small coupling, we obtain an approximate solution for a charged black hole of charge $Q$ and mass $M$. For $Q\ll M$ the validity of this solution extends down to the horizon. This allows us to explore the thermodynamic properties of the quadratic charged black hole and we find that, to our approximation, its thermodynamics is identical to that of a RN black hole. However our black hole's entropy is not equal to the one fourth of the horizon area. Finally we extend our analysis to the rotating charged black hole and qualitatively similar results are obtained.

Cauchy horizons, thermodynamics, and closed timelike curves in planar supersymmetric spaces.

We study geodesically complete, singularity free space-times induced by supersymmetric planar domain walls interpolating between Minkowski and anti-de Sitter ($AdS_4$) vacua. A geodesically complete space-time without closed time-like curves includes an infinite number of semi-infinite Minkowski space-times, separated from each other by a region of $AdS_4$ space-time. These space-times are closely related to the extreme Reissner Nordstr\" om (RN) black hole, exhibiting Cauchy horizons with zero Hawking temperature, but in contrast to the RN black hole there is no entropy. Another geodesically complete extension with closed time-like curves involves space-times connecting a finite number of semi-infinite Minkowski space-times.