The entropy function for the extremal Kerr-(anti-)de Sitter black holes

Based on Sen's entropy function formalism, we consider the Bekenstein-Hawking entropy of the extremal Kerr-(anti-)de Sitter black holes in 4-dimensions. Unlike the extremal Kerr black hole case with flat asymptotic geometry, where the Bekenstein-Hawking entropy S is proportional to the angular momentum J, we get a quartic algebraic relation between S and J by using the known solution to the Einstein equation. We recover the same relation in the entropy function formalism. Instead of full geometry, we write down an ansatz for the near horizon geometry only. The exact form of the unknown functions and parameters in the ansatz are obtained by solving the differential equations which extremize the entropy function. The results agree with the nontrivial relation between S and J.We also study the Gauss-Bonnet correction to the entropy exploiting the entropy function formalism. We show that the term, though being topological thus does not affect the solution, contributes a constant addition to the entropy because the term shifts the Hamiltonian by that amount.     

Anomalies and de Sitter radiation from the generic black holes in de Sitter spaces

Robinson–Wilczek's recent work shows that, the energy–momentum tensor flux required to cancel gravitational anomaly at the event horizon of a Schwarzschild-type black hole has an equivalent form to that of a (1+1)$(1+1)$-dimensional blackbody radiation at the Hawking temperature. Motivated by their work, Hawking radiation from the cosmological horizons of the general Schwarzschild–de Sitter and Kerr–de Sitter black holes, has been studied by the method of anomaly cancellation. The result shows that the absorbing gauge current and energy momentum tensor fluxes required to cancel gauge and gravitational anomalies at the cosmological horizon are precisely equal to those of Hawking radiation from it. It should be emphasized that the effective field theory for generic black holes in de Sitter spaces should be formulated within the region between the event horizon (EH) and the cosmological horizon (CH), to integrate out the classically irrelevant ingoing modes at the EH and the classically irrelevant outgoing modes at the CH, respectively.     

Entropy corrections to five-dimensional black holes and de Sitter spaces

It is shown that non-rotating black holes in three or four dimensions possess a canonical entropy. Recently study indicated that there were logarithmic corrections to Bekenstein–Hawking entropy in area with a uncertain coefficient which depends on specific models. In this paper, the thermal fluctuations on Bekenstein–Hawking entropy in five-dimensional topological AdS (TAds)-black holes and topological de Sitter (Tds) spaces will be considered based on a uniformly spaced area spectrum approach.     

Hawking radiation from black holes in de Sitter spaces via covariant anomalies

We apply the covariant anomaly cancellation method to compute the Hawking fluxes from the event and cosmic horizons of the Schwarzschild–de Sitter black hole. The derivation is new from the existing ones as we split the space in three different regions (near to and away from the event and cosmic horizons) and write down the covariant energy–momentum tensor using three step functions which covers the whole region leading elegantly to the conditions required to compute the Hawking fluxes from the event and cosmic horizons.     

Geometrothermodynamics for black holes and de Sitter space

A general method to extract thermodynamic quantities from solutions of the Einstein equation is developed. In 1994, Wald established that the entropy of a black hole could be identified as a Noether charge associated with a Killing vector of a global space-time (pseudo-Riemann) manifold. We reconstruct Wald’s method using geometrical language, e.g., via differential forms defined on the local space-time (Minkowski) manifold. Concurrently, the abstract thermodynamics are also reconstructed using geometrical terminology, which is parallel to general relativity. The correspondence between the thermodynamics and general relativity can be seen clearly by comparing the two expressions. This comparison requires a modification of Wald’s method. The new method is applied to Schwarzschild, Kerr, and Kerr–Newman black holes and de Sitter space. The results are consistent with previous results obtained using various independent methods. This strongly supports the validity of the area theorem for black holes.     

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.     

Pair production in Reissner-Nordstr(o)m-Anti de Sitter black holes

We studied the pair production of charged scalar particles of a five-dimensional near extremal Reissner-Nordstr(o)m-Anti de Sitter (RN-AdS5) black hole.The pair...     

Accelerating black holes in anti-de Sitter universe

A physical interpretation of theC-metric with a negative cosmological constantΛ is suggested. Using a convenient coordinate system it is demonstrated that this class of exact solutions of Einstein’s equations describes uniformly accelerating (possibly charged) black holes in anti-de Sitter universe. Main differences from the analogous de Sitter case are emphasised. Dedicated to my academic teacher Prof. J. Bičák on the occasion of his 60th birthday. This work was supported by the grant GACR-202/99/0261 of the Czech Republic and GAUK 141/2000 of Charles University in Prague.     

Thermodynamics of black holes in anti-de Sitter space

The Einstein equations with a negative cosmological constant admit black hole solutions which are asymptotic to anti-de Sitter space. Like black holes in asymptotically flat space, these solutions have thermodynamic properties including a characteristic temperature and an intrinsic entropy equal to one quarter of the area of the event horizon in Planck units. There are however some important differences from the asymptotically flat case. A black hole in anti-de Sitter space has a minimum temperature which occurs when its size is of the order of the characteristic radius of the anti-de Sitter space. For larger black holes the red-shifted temperature measured at infinity is greater. This means that such black holes have positive specific heat and can be in stable equilibrium with thermal radiation at a fixed temperature. It also implies that the canonical ensemble exists for asymptotically anti-de Sitter space, unlike the case for asymptotically flat space. One can also consider the microcanonical ensemble. One can avoid the problem that arises in asymptotically flat space of having to put the system in a box with unphysical perfectly reflecting walls because the gravitational potential of anti-de Sitter space acts as a box of finite volume.     

Thermodynamic properties of Reissner–Nordström–de Sitter quintessence black holes

Mass, electric charge, and temperature of black holes in the Reissner-Nordström-de Sitter quintessence (RN-dSQ) spacetime are obtained. The heat capacities of the RN-dSQ black hole for certain electric charge and mass are analyzed. The electrostatic energy and the dark energy in the RN-dSQ black hole are also calculated.     

Space-like submanifolds in the de Sitter spaces

In this paper, by using Cheng–Yau’s self-adjoint operator □, we study the space-like submanifolds in the de Sitter spaces and obtain some general rigidity results.     

具有双旋转参数5维黑洞的Cardy-Verlinde公式

对具有双旋转参数的5维时空中,黑洞视界的热力学参量与宇宙视界的热力学参量进行了研究 .发现宇宙视界的熵能写为Cardy-Verlinde公式的形式,而黑洞视界的熵要写成Cardy-Verl inde公式的形式,必须用Abbott 和Deser的方法,计算具有双旋转参数5维黑洞的质量.通过研究,给出了具有双旋转参数5维黑洞各热力学参量之间满足的关系式,即热力学第一定律的微分式. 关键词： Cardy-Verlinde公式 Casimir能量 de Sitter时空     

Cosmological black holes: A black hole in the Einstein-de Sitter universe

As an example of a dynamical cosmological black hole, a spacetime that describes an expanding black hole in the asymptotic background of the Einstein-de Sitter universe is constructed. The black hole is primordial in the sense that it forms ab initio with the big bang singularity and its expanding event horizon is represented by a conformal Killing horizon. The metric representing the black hole spacetime is obtained by applying a time dependent conformal transformation on the Schwarzschild metric, such that the result is an exact solution with a matter content described by a two-fluid source. Physical quantities such as the surface gravity and other effects like perihelion precession, light bending and circular orbits are studied in this spacetime and compared to their counterparts in the gravitational field of the isolated Schwarzschild black hole. No changes in the structure of null geodesics are recorded, but significant differences are obtained for timelike geodesics, particularly an increase in the perihelion precession and the non-existence of circular timelike orbits. The solution is expressed in the Newman-Penrose formalism.     

Time-dependent fluctuations and particle production in cosmological de Sitter and anti-de Sitter spaces

We study the evolution of time-dependent fluctuations and particle production in an expanding dS and contracting AdS universe. Using the functional Schrödinger formalism we are able to probe the time-dependent regime which is out of the reach of the standard approximations like the Bogolyubov method. In both cases, the evolution of fluctuations is governed by the harmonic oscillator equation with time-dependent frequency. In the case of an expanding dS universe we explicitly show that the frequency of fluctuations produced at a certain moment diminish in time, while the distribution of the created particles quickly approaches the thermal radiation of the dS space. In the case of a contracting AdS universe we show that the frequency of fluctuations produced at a certain moment grow in time. Nominally, the temperature of radiation diverges as the Big Crunch is approaching, however, increasing oscillations of the spectrum make the temperature poorly defined, which is in agreement with the fact that AdS space does not have an event horizon which would cause thermal radiation. Unlimited growth of fluctuations indicates that an eventual tunneling into AdS vacuum would have catastrophic consequences for our universe.