Entropy from near-horizon geometries of Killing horizons

TL;DR

This paper derives black hole entropy by analyzing near-horizon symmetries and algebraic structures, leading to the Bekenstein-Hawking entropy via the Cardy formula, highlighting a novel symmetry-based approach.

Contribution

It introduces a new method to compute black hole entropy using near-horizon symmetries and algebraic extensions, connecting geometric properties to conformal field theory techniques.

Findings

Identification of a Witt algebra of vector fields near the horizon

Derivation of a non-trivial central extension of the algebra

Reproduction of Bekenstein-Hawking entropy using the Cardy formula

Abstract

We derive black hole entropy based on the near-horizon symmetries of black hole space-times. To derive these symmetries we make use of an $(R,T)$-plane close to a Killing horizon. We identify a set of vector fields that preserves this plane and forms a Witt algebra. The corresponding algebra of Hamiltonians is shown to have a non-trivial central extension. Using the Cardy formula and the central charge we obtain the Bekenstein-Hawking entropy.