Universal properties from local geometric structure of Killing horizon

Details Universal properties from local geometric structure of Killing horizon Universal properties from local geometric structure of Killing horizon

2006-04-11

arxiv.org/abs/gr-qc/0604054v2

Class.Quant.Grav.24:3067-3084,2007

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

14 pages, v2. minor corrections

Scientific paper

10.1088/0264-9381/24/11/018

We consider universal properties that arise from a local geometric structure of a Killing horizon. We first introduce a non-perturbative definition of such a local geometric structure, which we call an asymptotic Killing horizon. It is shown that infinitely many asymptotic Killing horizons reside on a common null hypersurface, once there exists one asymptotic Killing horizon. The acceleration of the orbits of the vector that generates an asymptotic Killing horizon is then considered. We show that there exists the $\textit{diff}(S^1)$ or $\textit{diff}(R^1)$ sub-algebra on an asymptotic Killing horizon universally, which is picked out naturally based on the behavior of the acceleration. We also argue that the discrepancy between string theory and the Euclidean approach in the entropy of an extreme black hole may be resolved, if the microscopic states responsible for black hole thermodynamics are connected with asymptotic Killing horizons.

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