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.     

Geometro-thermodynamics of tidal charged black holes

Tidal charged spherically symmetric vacuum brane black holes are characterized by their mass m and tidal charge q, an imprint of the five-dimensional Weyl curvature. For q>0 they are formally identical to the Reissner–Nordström black hole of general relativity. We study the thermodynamics and thermodynamic geometries of tidal charged black holes and discuss similarities and differences as compared to the Reissner–Nordströ m black hole. As a similarity, we show that (for q>0) the heat capacity of the tidal charged black hole diverges on a set of measure zero of the parameter space, nevertheless both the regularity of the Ruppeiner metric and a Poincaré stability analysis show no phase transition at those points. The thermodynamic state spaces being different indicates that the underlying statistical models could be different. We find that the q<0 parameter range, which enhances the localization of gravity on the brane, is thermodynamically preferred. Finally we constrain for the first time the possible range of the tidal charge from the thermodynamic limit on gravitational radiation efficiency at black hole mergers.     

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.     

Black Hole Scattering via Spectral Methods

We present an alternative method to solve the problem of scattering by a black hole by adapting the spectral code originally developed by Boyd (Comp Phys 4:83, 1990). In order to show the effectiveness and versatility of the algorithm, we solve the scattering by Schwarzschild, standard acoustic, and charged black holes. We recover the partial and total absorption cross sections and, in the case of charged black holes, the conversion factor of eletromagnetic and gravitational waves. We also study the exponential decay of the reflection coefficient, which is a general feature of any scattering problem.     

Thermodynamics,phase transitions and Ruppeiner geometry for Einstein–dilaton–Lifshitz black holes in the presence of Maxwell and Born–Infeld electrodynamics

In this paper, we first obtain the higher-dimen-sional dilaton–Lifshitz black hole solutions in the presence of Born–Infeld (BI) electrodynamics. We find that there are two different solutions for the cases of \(z=n+1\) and \(z\ne n+1\) where z is the dynamical critical exponent and n is the number of spatial dimensions. Calculating the conserved and thermodynamical quantities, we show that the first law of thermodynamics is satisfied for both cases. Then we turn to the study of different phase transitions for our Lifshitz black holes. We start with the Hawking–Page phase transition and explore the effects of different parameters of our model on it for both linearly and BI charged cases. After that, we discuss the phase transitions inside the black holes. We present the improved Davies quantities and prove that the phase transition points shown by them are coincident with the Ruppeiner ones. We show that the zero temperature phase transitions are transitions in the radiance properties of black holes by using the Landau–Lifshitz theory of thermodynamic fluctuations. Next, we turn to the study of the Ruppeiner geometry (thermodynamic geometry) for our solutions. We investigate thermal stability, interaction type of possible black hole molecules and phase transitions of our solutions for linearly and BI charged cases separately. For the linearly charged case, we show that there are no phase transitions at finite temperature for the case \( z\ge 2\). For \(z<2\), it is found that the number of finite temperature phase transition points depends on the value of the black hole charge and there are not more than two. When we have two finite temperature phase transition points, there is no thermally stable black hole between these two points and we have discontinuous small/large black hole phase transitions. As expected, for small black holes, we observe finite magnitude for the Ruppeiner invariant, which shows the finite correlation between possible black hole molecules, while for large black holes, the correlation is very small. Finally, we study the Ruppeiner geometry and thermal stability of BI charged Lifshtiz black holes for different values of z. We observe that small black holes are thermally unstable in some situations. Also, the behavior of the correlation between possible black hole molecules for large black holes is the same as for the linearly charged case. In both the linearly and the BI charged cases, for some choices of the parameters, the black hole system behaves like a Van der Waals gas near the transition point.     

Charged fermions tunneling from regular black holes

We study Hawking radiation of charged fermions as a tunneling process from charged regular black holes, i.e., the Bardeen and ABGB black holes. For this purpose, we apply the semiclassical WKB approximation to the general covariant Dirac equation for charged particles and evaluate the tunneling probabilities. We recover the Hawking temperature corresponding to these charged regular black holes. Further, we consider the back-reaction effects of the emitted spin particles from black holes and calculate their corresponding quantum corrections to the radiation spectrum. We find that this radiation spectrum is not purely thermal due to the energy and charge conservation but has some corrections. In the absence of charge, e = 0, our results are consistent with those already present in the literature.     

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.     

Dark viscous fluid coupled with dark matter and future singularity

Motivated by Kerner and Man’s fermions tunneling method of dimension 4 black holes, in this paper, we further improve the analysis to investigate Hawking radiation of charged Dirac particles with spin 1/2 from general non-extremal rotating charged black holes with two parameters and a non-zero cosmological constant in minimal five-dimensional gauged supergravity. For space-times with different horizon topology and different dimensions, constructing a set of appropriate γ ^μ matrices for general covariant Dirac equation is an important technique for the fermion tunneling method. By introducing a set of appropriate matrices γ ^μ and employing the ansatz for the spin-up spinor field, we successfully recovered the tunneling probability of charged Dirac particles and the expected Hawking temperature of the black hole, which is exactly consistent with that obtained by other methods. Moreover, the fermion tunneling method can be directly applied to the other five-dimensional charged black holes, which strengthens the validity and power of the fermion tunneling method.     

Corrected Entropy of BTZ Black Holes

In this paper, corrected entropy of a class of BTZ black holes, include charge and rotation, studied. We obtain corrected Bekenstein-Hawking entropy and find that effect of charge viewed at order A ^?2, and effect of rotation viewed at order A ^?6, therefore Q and J don’t have contribution in corrected entropy lower than the second order. We also write the first law of black hole thermodynamics for the case of charged rotating BTZ black hole.     

Complexity growth rates for AdS black holes in massive gravity and <Emphasis Type="Italic">f</Emphasis>(<Emphasis Type="Italic">R</Emphasis>) gravity

The “complexity = action” duality states that the quantum complexity is equal to the action of the stationary AdS black hole within the Wheeler–DeWitt patch at late time approximation. We compute the action growth rates of the neutral and charged black holes in massive gravity and the neutral, charged and Kerr–Newman black holes in f(R) gravity to test this conjecture. Besides, we investigate the effects of the massive graviton terms, higher derivative terms and the topology of the black hole horizon on the complexity growth rate.     

Electromagnetic Quasinormal Modes in Hořava-Lifshitz Gravity

The electromagnetic quasinormal modes of Ho?ava-Lifshitz black hole is investigated by means of six-order WKB approach. We in this paper compare the quasinormal modes of this black hole with the charged black hole’s cases (we here take a regular charged black hole and Reissner-Nordström black hole for example). The numerical results of Ho?ava-Lifshitz’s quasinormal modes frequency show that the absolute value of imaginary part decrease as the parameter α increase. The fact means that charge in this spacetime make the quasinormal modes damp at a slower rate.     

Entropy and supersymmetry of D-dimensional extremal electric black holes versus string states

Following the work of Sen, we consider the correspondence between extremal black holes and string states in the context of the entropy. We obtain and study properties of electrically charged black hole backgrounds of tree level heterotic string theory compactified on a p-dimensional torus, for D = (10 − p) = 4,…,9. We study in particular a one-parameter extremal class of these black holes, the members of which are shown to be supersymmetric. We find that the entropy of such an extremal black hole, when calculated at the stringy stretched horizon, scales in such a way that it can be identified with the entropy of the elementary string state with the corresponding quantum numbers.     

A rotating charged black hole solution in f(R) gravity

In the context of f(R) theories of gravity, we address the problem of finding a rotating charged black hole solution in the case of constant curvature. A new metric is obtained by solving the field equations and we show that its behaviour is typical of a rotating charged source. In addition, we analyse the thermodynamics of the new black hole. The results ensure that the thermodynamical properties in f(R) gravities are qualitatively similar to those of standard General Relativity.     

(2 + 1)-Dimensional Solutions in F(R) Gravity

Motivated by the well-known charged BTZ black holes, we look for (2 + 1)-dimensional solutions of F(R) gravity. At first we investigate some near horizon solutions and after that we obtain asymptotically Lifshitz black hole solutions. Finally, we discuss about rotating black holes with exponential form of F(R) theory.     

The information paradox: Conflicts and resolutions

Many relativists have been long convinced that black hole evaporation leads to information loss or remnants. String theorists have however not been too worried about the issue, largely due to a belief that the Hawking argument for information loss is flawed in its details. A recently derived inequality shows that the Hawking argument for black holes with horizon can in fact be made rigorous. What happens instead is that in string theory, black hole microstates have no horizons. Thus the evolution of radiation quanta with E??kT is modified by order unity at the horizon, and we resolve the information paradox.     

Quantum Corrections for Regular Black Holes with Charge and Coupling Constant

In this paper, we use semi-classical tunneling approach to calculate the quantum corrections to the Hawking temperature as well as entropy of the Kehagias-Sftesos asymptotically flat black hole solution and charged regular black hole with Fermi-Dirac distribution. For this purpose, we apply the first law of black hole thermodynamics to investigate the semi-classical entropy of both black holes having mass as well as charge or coupling constant. For both black holes, the entropy corrections contain the logarithmic term as a leading order correction term. For Kehagias-Sftesos asymptotically flat black hole, the semi-classical Hawking temperature and black hole entropy will behave asymptotically by considering the vanishing coupling constant b = 0. We have obtained the same analysis for the corrected thermodynamical quantities for this BH. For charged regular black hole with Fermi-Dirac distribution, if we neglect the charged effects in our analysis, i.e., q = 0, then these corrections approximately leads to the Schwarzschild black hole which is already given in the literature.     

Relaxation dynamics of charged gravitational collapse

We study analytically the relaxation dynamics of charged test fields left outside a newly born charged black hole. In particular, we obtain a simple analytic expression for the fundamental quasinormal resonances of near-extremal Reissner-Nordström black holes. The formula is expressed in terms of the black-hole physical parameters: , where TBH and Φ are the temperature and electric potential of the black hole, and q is the charge of the field.     

Cosmological solutions with charged black holes

We consider the problem of constructing cosmological solutions of the Einstein–Maxwell equations that contain multiple charged black holes. By considering the field equations as a set of constraint and evolution equations, we construct exact initial data for N charged black holes on a hypersphere. This corresponds to the maximum of expansion of a cosmological solution, and provides sufficient information for a unique evolution. We then consider the specific example of a universe that contains eight charged black holes, and show that the existence of non-zero electric charge reduces the scale of the cosmological region of the space. These solutions generalize the Majumdar–Papapetrou solutions away from the extremal limit of charged black holes, and provide what we believe to be some of the first relativistic calculations of the effects of electric charge on cosmological backreaction.     

Entropy of an extremal regular black hole

We introduce a magnetically charged extremal regular black hole in the coupled system of Einstein gravity and nonlinear electrodynamics. Its near horizon geometry is given by AdS₂×S²${\mathit{AdS}}_2\times S^2$. It turns out that the entropy function approach does not automatically lead to a correct entropy of the Bekenstein–Hawking entropy. This contrasts to the case of the extremal Reissner–Norström black hole in the Einstein–Maxwell theory. We conclude that the entropy function approach does not work for a magnetically charged extremal regular black hole without singularity, because of the nonlinearity of the entropy function.     

4D localization in Randall-Sundrum 2 supergravity and in Vasiliev theories

We discuss the problem of localization of 4D massless states in Randall-Sundrum 2 (one-brane) models. A Randall-Sundrum 2 construction starting from N=8 gauged supergravity in 5D anti-de Sitter space gives rise to an N=4 supergravity-matter system. We explicitly show that only the modes of the N=4 graviton supermultiplet localize on the 4D brane, streamlining and generalizing previous works. We also point out that while charged 1/4 BPS black holes do exist in the 4D theory, they are always produced in sets of total charge zero. This zero-charge configuration uplifts to a 5D metric without naked singularities, thus avoiding the curvature singularity of the 5D uplift of an isolated charged BPS black hole. Finally, we resolve a puzzle with localization of massless high spin fields on a (putative) Randall-Sundrum 2 construction based on Vasiliev?s high spin theories. We show that while high spin fields do localize, the gauge symmetry that ensures decoupling of their unphysical polarizations is anomalous. This implies that the high spin fields must acquire a mass.