Conformal entropy as a consequence of the properties of stationary Killing horizons

TL;DR

This paper derives the microscopic black hole entropy formula from properties of stationary Killing horizons, revealing a geometric origin for the near horizon conformal symmetry and its implications for entropy calculations.

Contribution

It demonstrates that the Virasoro algebra-based entropy formula can be obtained solely from stationary Killing horizon properties, clarifying the geometric basis of near horizon conformal symmetry.

Findings

Entropy formula derived from horizon properties

Near horizon conformal symmetry has a geometric origin

Explicit power expansion near the horizon

Abstract

We show that microscopic black hole entropy formula based on Virasoro algebra can be derived from usual properties of stationary Killing horizons alone and absence of singularities of curvature invariants on them. In such a way some usual additional assumptions are shown to be fulfilled. In addition, for all quantities power expansion near horizon and thus explicit insight of the limiting procedure is given. More important the near horizon conformal symmetry proposed by Carlip together with its consequences on microscopic entropy is given a clear geometric origin.