Supermembranes on black holes

We report a new family of supermembrane vacua possesing the Siegel symmetry. This family consists of bosonic solutions of supermembrane field equations and describes static, toroidal membranes in d=11 black hole spacetimes. The black holes we consider are obtained by embedding the d=4 Reissner-Nordström solutions into d=11, N=1 supergravity. We show that supermembranes pick, as their backgrounds, only the extreme Reissner-Nordström black holes and require the d=4 magnetic charge to be non-zero. Moreover, the membranes on dyonic holes can be interpreted, at the linearized level, as fluctuations of the membranes on magnetically charged holes. The quantisation around the toroidal membranes on the magnetically charged, extreme black holes therefore poses itself as an interesting problem.     

Magnetic charge,black holes,and cosmic censorship

The possibility of converting a Reissner-Nordström black hole into a naked singularity by means of test particle accretion is considered. The dually charged Reissner-Nordström metric describes a black hole only when M² > Q³ + P². The test particle equations of motion are shown to allow test particles with arbitrarily large magnetic charge/mass ratios to fall radially into electrically charged black holes. To determine the nature of the final state (black hole or naked singularity) an exact solution of Einstein's equations representing a spherical shell of magnetically charged dust falling into an electrically charged black hole is studied. Naked singularities are never formed so long as the weak energy condition is obeyed by the infalling matter. The differences between the spherical shell model and an infalling point test particle are examined and discussed.     

Arbitrary dimensional cosmological multi-black holes

We find cosmological black hole solutions for spacetimes of arbitrary dimension (greater than three) that are asymptotically de Sitter, and we show that these solutions can be extended to give multi-black hole solutions. We investigate the motion of a charged massive test particle in a five-dimensional extreme Reissner-Nordström de Sitter background. Furthermore we obtain Killing spinors for Reissner-Nordström de Sitter spacetimes. We also find five-dimensional cosmological black hole solutions in an asymptotically anti de Sitter spacetime and we show that these solutions are supersymmetric in the sense that they admit a supercovariantly constant spinor.     

Higher dimensional Reissner-Nordström-FRW metric

By inspecting some known solutions to Einstein's equations, we present the metric of higher dimensional Reissner-Nordström black hole in the background of a Friedman-Robertson-Walker universe. Then we verify the solution with a perfect fluid. The discussion of the event horizon of the black hole reveals that the scale of the black hole would increase with the expansion of the universe and decrease with the contraction of the universe.     

Hawking Radiation of Charged Particles via Tunneling from Arbitrarily Dimensional Reissner-Nordström Black Holes

Parikh-Wilzcek’s recent work, which treats the Hawking radiation as semi-classical tunneling process from the event horizon of four dimensional Schwarzshild and Reissner- Nordström black hole, indicates that self-gravitation gives a correction to the Hawking precisely thermal spectrum and the tunneling rate is related to the change of Bekenstein- Hawking, but satisfies the underlying unitary theory. In this paper, we extend the model to study the Hawking radiation of charged particles via tunneling from arbitrarily dimensional Reissner-Nordström black holes, and obtain the same result as Parikh-Wilzcek’s. Meanwhile, in this framework, we point out that the first law of the black hole thermodynamics is reliable and the information conservation is only suitable for the reversible process.     

Hawking Radiation of Black Hole in Einstein-Proca Theory

The Hawking radiation of black hole in Einstein-Proca theory is discussed in this paper. The Einstein-Proca black hole is more general than Reissner-Nordström black hole, because Proca field is massive vector field. We calculate several quantum perturbations in this spacetime, and obtain the Hawking radiation at the horizon in Einstein-Proca theory.     

Observational effects in black and white holes (dynamical wormholes)

The models of wormholes with a topology based on a Reissner-Nordström black and white hole are considered. In these models, there are one entrance in one universe (a black hole) and one exit into another universe (a white hole) corresponding to this entrance. The passage of matter through the wormhole in these models is possible only in one direction (from past to future). All models are considered under the assumption of spherical symmetry. It is shown that all models without a throat do not violate the null energy condition. The model of a Reissner-Nordström black hole containing no singularities inside the horizon has been constructed. The trajectories of particles and light rays passing from one universe into another have been constructed for the simplest Reissner-Nordström black and white hole. Distinctive features have been found for the images of objects from another universe observed through such objects. The characteristics of these images are compared with those for ordinary wormholes.     

Entropy of Non-stationary and Slowly Changing Reissner-Nordström Black Hole

Simplifying Dirac equation near the horizon, Hawking temperature is obtained by applying a new tortoise coordinate transformation. Using the improved thin film brick-wall model and WKB approximation, the entropy of Dirac field in the non-stationary and slowly changing Reissner-Nordström black hole is calculated. The result shows that the entropy of the black hole is still proportional to the horizon area, and black hole entropy is just identical to the entropy of the quantum state at the horizon. In addition, the new tortoise coordinate transformation can make the cut-off parameter introduced in solving the entropy of non-stationary black hole simplified to the same as that in the static and stationary cases.     

Thermodynamics of Black Holes in Einstein-Maxwell-Gauss-Bonnet Theory

We study the black hole solution in Einstein-Maxwell-Gauss-Bonnet (EMGB) gravity theory with a cosmological constant in five dimension. It is a generalization of the Reissner-Nordström-de Sitter (RNdS) or RNAdS (Reissner-Nordström-Anti-de Sitter) black hole solutions (according as the cosmological constant is positive or negative) in the Einstein-Gauss-Bonnet (EGB) theory. We analyze the thermodynamic quantities of EMGB black hole and find a restriction involving the charge and the cosmological constant for the existence of an extremal black hole. Finally, Hawking-Page phase transition has been discussed for the present black hole.     

Quantum corrections to the entropy of charged rotating black holes

Hawking radiation from a black hole can be viewed as quantum tunneling of particles through the event horizon. Using this approach we provide a general framework for studying corrections to the entropy of black holes beyond semiclassical approximations. Applying the properties of exact differentials for three variables to the first law thermodynamics, we study charged rotating black holes and explicitly work out the corrections to entropy and horizon area for the Kerr–Newman and charged rotating BTZ black holes. It is shown that the results for other geometries like the Schwarzschild, Reissner-Nordström and anti-de Sitter–Schwarzschild spacetimes follow easily.     

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.     

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.     

Hawking Radiation of the Charged Particle Via Tunneling from the Reissner-Nordström Black Hole

Since Parikh and Wilczek proposed a semiclassical tunneling method to investigate the Hawking radiation of static and spherically symmetric black holes, the method has been extensively developed to study various black holes. However, in almost all of the subsequent papers, there exists a important shortcoming that the geodesic equation of the massive particle is defined inconsistently with that of the massless particle. In this paper, we propose a new idea to reinvestigate the tunneling radiation from the event horizon of the Reissner-Nordström black hole. In our treatment, by starting from the Lagrangian analysis on the action, we redefine the geodesic equation of the massive and massless particle via tunneling from the event horizon of the Reissner-Nordström black hole, which overcomes the shortcoming mentioned above. The highlight of our work is a new and important development for the Parikh-Wilczek’s semiclassical tunneling method.     

Two-Mode Harmonic Oscillator Model of Reissner-Nordström Black Hole

In this paper, we will assume that the Reissner-Nordström black hole can be dynamically expressed, at the classical level, in terms of a reduced phase space consisting of the physical observables and their canonical conjugates. More specifically, we propose that the phase space can be described by the black hole’s mass and charge along with their respective conjugates. In this four-dimensional phase space we perform a couple of canonical transformations to obtain a two-mode harmonic oscillator model of Reissner-Nordström black hole. By adopting this model, the quantum spectrum and wave function of horizon area are presented.     

Quantum Anomaly and Hawking Radiation of Charged and Magnetized Reissner-Nordström de Sitter Black Hole

The recent work of Robinson and Wilczek that Hawking radiation can be determined by the compensating fluxes is extended to the charged and magnetized Reissner-Nordström de Sitter black hole. We reconstruct the electromagnetic field tensor and the Lagrangian of the field corresponding to the source with electric and magnetic charges to redefine an equivalent charge and gauge potential. We construct the effect field theory between the event horizon and cosmological horizon to respectively determine the compensating fluxes from them, which are shown to exactly equal to those of Hawking radiation, by the covariant anomaly cancellation conditions.     

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.     

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.     

Hawking Radiation of the Charged Particles via Tunneling from the (<Emphasis Type="Italic">n</Emphasis>+2)-Dimensional Topological Reissner-Nordström-de Sitter Black Hole

Extending Parikh-Wilczek’s semi-classical tunneling method, we discuss the Hawking radiation of the charged massive particles via tunneling from the cosmological horizon of (n+2)-dimensional Topological Reissner-Nordström-de Sitter black hole.The result shows that, when energy conservation and electric charge conservation are taken into account, the derived spectrum deviates from the pure thermal one, but satisfies the unitary theory, which provides a probability for the solution of the information loss paradox.     

Acceleration of particles by nonrotating charged black holes?

Recently, in the series of works a new effect of acceleration of particles by black holes has been found. Under certain conditions, the energy in the center-of-mass system can become infinitely large. The essential ingredient of such effect is the rotation of a black hole. In this work, it has been argued that the similar effect exists for a nonrotating but charged black hole even for the simplest case of radial motion of particles in the Reissner-Nordström background. All main features of the effect under discussion due to rotating black holes have their counterpart for the nonrotating charged ones.     

The Thermal Radiation from Static Spherically Symmetric Black Holes

By use of the radiant emittance near the event horizon of static spherically symmetric black hole, the radiation field around the black hole was studied and found the generalized Stefan Boltzmann coefficient σ of thermal radiation near the event horizon is much greater than the flat space-time blackbody radiation. For Schwarzschild black hole, σ will increased as the black hole mass increases. For Reissner-Nordström black hole, σ has some relation with the quality and the charges of the black hole. Thermal particle model was proposed creatively to study the radiation power and radiant energy flux of static spherically symmetric black hole, found when η take the inherent thickness, for all Schwarzschild black hole the radiation power are the same and the radiant energy flux is inversely proportional to the square of the distance from observer to the black hole, for Reissner-Nordström black hole the radiation power is associated with the quality and the charge of the black hole. When given the mass and charges of the black hole, the radiant energy flux is inversely proportional to the square of the distance from observer to the black hole.