Dirty black holes: Symmetries at stationary nonstatic horizons

Classical and Quantum Gravity, 2004

We consider the spacetime geometry of a static but otherwise generic black hole (that is, the horizon geometry and topology are not necessarily spherically symmetric). It is demonstrated, by purely geometrical techniques, that the curvature tensors, and the Einstein tensor in particular, exhibit a very high degree of symmetry as the horizon is approached. Consequently, the stress-energy tensor will be highly constrained near any static Killing horizon. More specifically, it is shown that -at the horizon -the stress-energy tensor blockdiagonalizes into "transverse" and "parallel" blocks, the transverse components of this tensor are proportional to the transverse metric, and these properties remain invariant under static conformal deformations. Moreover, we speculate that this geometric symmetry underlies Carlip's notion of an asymptotic near-horizon conformal symmetry controlling the entropy of a black hole.

Journal of Physics: Conference Series, 2006

Using Virasoro algebra approach, black hole entropy formula for a general class of higher curvature Lagrangians with arbitrary dependence on Riemann tensor can be obtained from properties of stationary Killing horizons. The properties used are a consequence of regularity of invariants of Riemann tensor on the horizon. As suggested by an example Lagrangian, eventual generalisation of these results to Lagrangians with derivatives of Riemann tensor, would require assuming regularity of invariants involving derivatives of Riemann tensor and that would lead to additional restrictions on metric functions near horizon.

Physical Review D, 1999

We develop a method for computing the free-energy of a canonical ensemble of quantum fields near the horizon of a rotating black hole. We show that the density of energy levels of a quantum field on a stationary background can be related to the density of levels of the same field on a fiducial static space-time. The effect of the rotation appears in the additional interaction of the "static" field with a fiducial abelian gauge-potential. The fiducial static space-time and the gauge potential are universal, i.e., they are determined by the geometry of the given physical spacetime and do not depend on the spin of the field. The reduction of the stationary axially symmetric problem to the static one leads to a considerable simplification in the study of statistical mechanics and we use it to draw a number of conclusions. First, we prove that divergences of the entropy of scalar and spinor fields at the horizon in the presence of rotation have the same form as in the static case and can be removed by renormalization of the bare black hole entropy. Second, we demonstrate that statistical-mechanical representation of the Bekenstein-Hawking entropy of a black hole in induced gravity is universal and does not depend on the rotation.

2019

We prove that non-extremal black holes in four-dimensional general relativity exhibit an infinite-dimensional symmetry in their near horizon region. By prescribing a physically sensible set of boundary conditions at the horizon, we derive the algebra of asymptotic Killing vectors, which is shown to be infinite-dimensional and includes, in particular, two sets of supertranslations and two mutually commuting copies of the Virasoro algebra. We define the surface charges associated to the asymptotic diffeomorphisms that preserve the boundary conditions and discuss the subtleties of this definition, such as the integrability conditions and the correct definition of the Dirac brackets. When evaluated on the stationary solutions, the only non-vanishing charges are the zero-modes. One of them reproduces the Bekenstein-Hawking entropy of Kerr black holes. We also study the extremal limit, recovering the NHEK geometry. In this singular case, where the algebra of charges and the integrability ...

Classical and Quantum Gravity, 2005

Physical Review D, 2012

We consider generic, or "dirty" (surrounded by matter), stationary rotating black holes with axial symmetry. The restrictions are found on the asymptotic form of metric in the vicinity of non-extremal, extremal and ultra-extremal horizons, imposed by the conditions of regularity of increasing strength: boundedness on the horizon of the Ricci scalar, of scalar quadratic curvature invariants, and of the components of the curvature tensor in the tetrad attached to a falling observer.

Physical Review D, 1992

Considerable interest has recently been expressed in (static spherically symmetric) blackholes in interaction with various classical matter fields (such as electromagnetic fields, dilaton fields, axion fields, Abelian Higgs fields, non-Abelian gauge fields, etc). A common feature of these investigations that has not previously been remarked upon is that the Hawking temperature of such systems appears to be suppressed relative to that of a vacuum blackhole of equal horizon area. That is: kT H ≤h/(4πr H) ≡h/ √ 4πA H. This paper will argue that this suppression is generic.

Physical Review D, 1998

We consider the thermodynamic properties of the constant curvature black hole solution recently found by Bañados. We show that it is possible to compute the entropy and the quasilocal thermodynamics of the spacetime using the Einstein-Hilbert action of General Relativity. The constant curvature black hole has some unusual properties which have not been seen in other black hole spacetimes. The entropy of the black hole is not associated with the event horizon; rather it is associated with the region between the event horizon and the observer. Further, surfaces of constant internal energy are not isotherms so the first law of thermodynamics exists only in an integral form. These properties arise from the unusual topology of the Euclidean black hole instanton. 04.70.Dy, 04.20.Ha, 04.70.Bw * An examination of all identifications in four dimensional anti-de Sitter spacetime has been presented by Holst and Peldan [3], but the global properties of their black hole solution differ from those of the solution found by Bañados.

Physical review D: Particles and fields, 1993

It is by now clear that the naive rule for the entropy of a black hole, (entropy) = 1/4 (area of event horizon), is violated in many interesting cases. Indeed, several authors have recently conjectured that in general the entropy of a dirty black hole might be given purely in terms of some surface integral over the event horizon of that black hole. A formal proof of this conjecture, using Lorentzian signature techniques, has recently been provided by Wald. This note performs two functions. Firstly, by extending a previous analysis due to the present author [Physical Review D48, ???? (15 July 1993)] it is possible to provide a rather different proof of this result-a proof based on Euclidean signature techniques. The proof applies both to arbitrary static [aspheric] black holes, and also to arbitrary stationary axisymmetric black holes. The total entropy is note proceeds via Euclidean signature techniques the result can be checked against certain special cases previously obtained by other techniques, e.g. (Ricci) n gravity, R n gravity, and Lovelock gravity.

Classical and Quantum Gravity, 2005

Equilibrium states of black holes can be modelled by isolated horizons. If the intrinsic geometry is spherical, they are called type I while if it is axi-symmetric, they are called type II. The detailed theory of geometry of quantum type I horizons and the calculation of their entropy can be generalized to type II, thereby including arbitrary distortions and rotations. The leading term in entropy of large horizons is again given by 1/4th of the horizon area for the same value of the Barbero-Immirzi parameter as in the type I case. Ideas and constructions underlying this extension are summarized.