Entropies of a Toroidal Black Hole Due to Scalar and Dirac Fields

Using the thin film brick-wall model, the entropies of a toroidal black hole due to scalar and Dirac fields are investigated. The entropy due to the scalar field is one fourth of the horizon area, and that due to the Dirac field is seven eighth of the area. These results are similar to that in black holes with horizon topology S ². The cutoff in toroidal black hole is chosen as the same as one in black holes with horizon topology S ², which seems to mean that the thin film brick-wall model is universal.     

A Generalization of Hawking’s Black Hole Topology Theorem to Higher Dimensions

Hawking’s theorem on the topology of black holes asserts that cross sections of the event horizon in 4-dimensional asymptotically flat stationary black hole spacetimes obeying the dominant energy condition are topologically 2-spheres. This conclusion extends to outer apparent horizons in spacetimes that are not necessarily stationary. In this paper we obtain a natural generalization of Hawking’s results to higher dimensions by showing that cross sections of the event horizon (in the stationary case) and outer apparent horizons (in the general case) are of positive Yamabe type, i.e., admit metrics of positive scalar curvature. This implies many well-known restrictions on the topology, and is consistent with recent examples of five dimensional stationary black hole spacetimes with horizon topology S ² × S ¹. The proof is inspired by previous work of Schoen and Yau on the existence of solutions to the Jang equation (but does not make direct use of that equation).     

The Dynamics of Apparent Horizons in Robinson–Trautman Spacetimes

We present an alternative scheme of finding apparent horizons based on spectral methods applied to Robinson–Trautman spacetimes. We have considered distinct initial data such as representing the spheroids of matter and the head-on collision of two non-rotating black holes. The evolution of the apparent horizon is presented. We have obtained in some cases a mass gap between the final Bondi and apparent horizon masses, whose implications were briefly commented in the light of the thermodynamics of black holes.     

Area invariance of apparent horizons under arbitrary Lorentz boosts

It is a well known analytic result in general relativity that the 2-dimensional area of the apparent horizon of a black hole remains invariant regardless of the motion of the observer, and in fact is independent of the t = constant slice, which can be quite arbitrary in general relativity. Nonetheless the explicit computation of horizon area is often substantially more difficult in some frames (complicated by the coordinate form of the metric), than in other frames. Here we give an explicit demonstration for very restricted metric forms of (Schwarzschild and Kerr) vacuum black holes. In the Kerr–Schild coordinate expression for these spacetimes they have an explicit Lorentz-invariant form. We consider boosted versions with the black hole moving through the coordinate system. Since these are stationary black hole spacetimes, the apparent horizons are two dimensional cross sections of their event horizons, so we compute the areas of apparent horizons in the boosted space with (boosted) t = constant, and obtain the same result as in the unboosted case. Note that while the invariance of area is generic, we deal only with black holes in the Kerr–Schild form, and consider only one particularly simple change of slicing which amounts to a boost. Even with these restrictions we find that the results illuminate the physics of the horizon as a null surface and provide a useful pedagogical tool. As far as we can determine, this is the first explicit calculation of this type demonstrating the area invariance of horizons. Further, these calculations are directly relevant to transformations that arise in computational representation of moving black holes. We present an application of this result to initial data for boosted black holes.     

Direct imaging rapidly-rotating non-Kerr black holes

Recently, two of us have argued that non-Kerr black holes in gravity theories different from General Relativity may have a topologically non-trivial event horizon. More precisely, the spatial topology of the horizon of non-rotating and slow-rotating objects would be a 2-sphere, like in Kerr space–time, while it would change above a critical value of the spin parameter. When the topology of the horizon changes, the black hole central singularity shows up. The accretion process from a thin disk can potentially overspin these black holes and induce the topology transition, violating the Weak Cosmic Censorship Conjecture. If the astrophysical black hole candidates are not the black holes predicted by General Relativity, we might have the quite unique opportunity to see their central region, where classical physics breaks down and quantum gravity effects should appear. Even if the quantum gravity region turned out to be extremely small, at the level of the Planck scale, the size of its apparent image would be finite and potentially observable with future facilities.     

Asymptotically FRW black holes

Special solutions of the LTB family representing collapsing over-dense regions corresponding to asymptotically closed, open, or flat FRW models are found. These solutions may be considered as representing dynamical mass condensations leading to black holes immersed in a FRW universe. We study the dynamics of the collapsing region, and its density profile. The question of the strength of the central singularity and its nakedness, as well as the existence of an apparent horizon and an event horizon is dealt with in detail, shedding light to the notion of cosmological black holes. Differences to the Schwarzschild black hole are addressed.     

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.     

On EVH black hole solution in heterotic string theory

We study the near horizon geometry of charged rotating black holes in toroidal compactifications of heterotic string theory. We analyze the extremal vanishing horizon (EVH) limit for these black hole solutions and we will show that the near horizon geometry develops an AdS₃ throat. Furthermore, we will show that the near horizon limit of near EVH black holes has a BTZ factor. We also comment on the CFT dual to this near horizon geometry.     

Possible effects of a cosmological constant on black hole evolution

We explore possible effects of vacuum energy on the evolution of black holes. If the universe contains a cosmological constant, and if black holes can absorb energy from the vacuum, then black hole evaporation could be greatly suppressed. For the magnitude of the cosmological constant suggested by current observations, black holes larger than 4×10²⁴ g would accrete energy rather than evaporate. In this scenario, all stellar and supermassive black holes would grow with time until they reach a maximum mass scale of 6×10⁵⁵ g, comparable to the mass contained within the present day cosmological horizon.     

Limits to the Acceleration of Black Holes

Using the Dirac equation but with a null surfacecondition, we obtain the event horizon equation, and thetemperature function of a rectilinearly acceleratingblack hole with electric-magnetic charge. The cosmic censorship hypothesis implies that theacceleration of a black hole has a limit, which isM/r_H ² for the rectilinearlyaccelerating black hole. The limit values ofacceleration for other black holes, including the rectilinearly accelerating blackhole with electricmagnetic charge the Kerr–Newmanblack hole, and the Kerr black hole are given.     

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.     

Rediscussion of charged dilaton-axion black hole entropy

We rediscuss the entropy of a charged dilaton-axion black hole for both the asymptotically flat and non-flat cases by using the thin film brick-wall model. This improved method avoids some drawbacks in the original brick-wall method such as the small mass approximation, neglecting the logarithm term, and taking the term L ³ as the contribution of the vacuum surrounding the black hole. The entropy we obtain turns out to be proportional to the horizon area of the black hole, conforming to the Bekenstein-Hawking area-entropy formula for black holes.      

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.     

How do black holes predict the sign of the Fourier coefficients of siegel modular forms?

Single centered supersymmetric black holes in four dimensions have spherically symmetric horizon and hence carry zero angular momentum. This leads to a specific sign of the helicity trace index associated with these black holes. Since the latter are given by the Fourier expansion coefficients of appropriate meromorphic modular forms of Sp(2,\mathbbZ){Sp(2,{\mathbb{Z}})} or its subgroup, we are led to a specific prediction for the signs of a subset of these Fourier coefficients which represent contributions from single centered black holes only. We explicitly test these predictions for the modular forms which compute the index of quarter BPS black holes in heterotic string theory on T ⁶, as well as in \mathbbZ_N{{\mathbb{Z}}_N} CHL models for N = 2, 3, 5, 7.     

The closed trapped region and the apparent horizon of two Schwarzschild black holes

The problem of two Schwarzschild black holes on a time-symmetric spacelike hypersurface is investigated. The location of the closed trapped region and the apparent horizon is calculated. It is shown that the topology of the closed trapped region is not as previously believed.     

Domain with Noncompactified Extra Dimensions in the Multidimensional Universe with Compactified Extra Dimensions

It is argued that in our Universe with compactified extra dimensions (ED) also domains exist with noncompactified ED. The multidimensional gravity (MD) on the principal bundle with structural group SU(3) is considered and a spherically symmetric solution in this theory is obtained. This solution is a wormhole-like object located between two null surfaces ds² = 0 and can be considered as a domain with noncompactified ED which is sewn to a 4D spacetime with compactified ED. In some sense these solutions are dual to black holes: they represent static spherically symmetric solutions under null surfaces, whereas black holes are static spherically symmetric solutions outside the event horizon.     

D = 5 Einstein-Maxwell-Chern-Simons black holes

Five-dimensional Einstein-Maxwell-Chern-Simons theory with a Chern-Simons coefficient lambda = 1 has supersymmetric black holes with a vanishing horizon angular velocity but finite angular momentum. Here supersymmetry is associated with a borderline between stability and instability, since for lambda > 1 a rotational instability arises, where counterrotating black holes appear, whose horizon rotates in the opposite sense to the angular momentum. For lambda > 2 black holes are no longer uniquely characterized by their global charges, and rotating black holes with vanishing angular momentum appear.     

Anomaly analysis of Hawking radiation from Kaluza–Klein black hole with squashed horizon

Considering gravitational and gauge anomalies at the horizon, a new method to derive Hawking radiation from black holes has been developed by Wilczek et al. In this paper, we apply this method to non-rotating and rotating Kaluza–Klein black holes with squashed horizon, respectively. For the rotating case, we found that, after dimensional reduction, an effective U(1) gauge field is generated by an angular isometry. The results show that the gauge current and energy-momentum tensor fluxes are exactly equivalent to Hawking radiation from the event horizon.     

Novel CFT duals for extreme black holes

In this paper, we study the CFT duals for extreme black holes in the stretched horizon formalism. We consider the extremal RN, Kerr-Newman-AdS-dS, as well as the higher dimensional Kerr-AdS-dS black holes. In all these cases, we reproduce the well-established CFT duals. Actually we show that for stationary extreme black holes, the stretched horizon formalism always gives rise to the same dual CFT pictures as the ones suggested by ASG of corresponding near horizon geometries. Furthermore, we propose new CFT duals for 4D Kerr-Newman-AdS-dS and higher dimensional Kerr-AdS-dS black holes. We find that every dual CFT is defined with respect to a rotation in certain angular direction, along which the translation defines a U(1) Killing symmetry. In the presence of two sets of U(1) symmetry, the novel CFT duals are generated by the modular group SL(2,Z), and for n sets of U(1) symmetry there are general CFT duals generated by T-duality group SL(n,Z).     

Holography at an extremal De Sitter horizon

Rotating maximal black holes in four-dimensional de Sitter space, for which the outer event horizon coincides with the cosmological horizon, have an infinite near-horizon region described by the rotating Nariai metric. We show that the asymptotic symmetry group at the spacelike future boundary of the near-horizon region contains a Virasoro algebra with a real, positive central charge. This is evidence that quantum gravity in a rotating Nariai background is dual to a two-dimensional Euclidean conformal field theory. These results are related to the Kerr/CFT correspondence for extremal black holes, but have two key differences: one of the black hole event horizons has been traded for the cosmological horizon, and the near-horizon geometry is a fiber over dS₂ rather than AdS₂.