Universal properties from local geometric structure of Killing horizon

TL;DR

This paper introduces the concept of asymptotic Killing horizons to explore universal geometric properties of Killing horizons, revealing a natural algebraic structure and potential links to black hole entropy in string theory.

Contribution

It defines asymptotic Killing horizons non-perturbatively, shows their universal algebraic structure, and suggests a connection to black hole entropy discrepancies.

Findings

Existence of infinitely many asymptotic Killing horizons on a null hypersurface.

Universal $ extit{diff}(S^1)$ or $ extit{diff}(R^1)$ algebra on these horizons.

Potential resolution of entropy discrepancies in extreme black holes.

Abstract

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.