Algebra of Universal Horizon Preserving Diffeomorphisms

TL;DR

This paper investigates the algebra of diffeomorphisms that preserve universal horizons in modified gravity theories, extending the near horizon symmetry approach used for Killing horizons to universal horizons in Hořava-Lifshitz gravity.

Contribution

It computes the classical algebra of universal horizon preserving diffeomorphisms, revealing similarities and differences with the Killing horizon case, advancing understanding of horizon thermodynamics.

Findings

Algebra similar to Killing horizon case

Modification consistent with universal horizon thermodynamics

Provides groundwork for entropy calculation via symmetry methods

Abstract

In relativistic gravity, requiring a spacetime hypersurface be a Killing horizon breaks the general covariance of general relativity. The residual algebra of horizon preserving diffeomorphisms can be extended to a Virasoro algebra near the horizon, the central charge of which yields the Bekenstein-Hawking entropy via the Cardy formula. This near horizon symmetry approach provides an argument for why black hole entropy computations in various quantum gravity models all agree. An exception may be Ho\v{r}ava-Lifshitz gravity, where causal horizons are not Killing horizons but rather universal horizons. As a first step towards determining if the entropy of universal horizons can be calculated by a near horizon symmetry approach we compute the classical algebra of universal horizon preserving diffeomorphisms. We find that the algebra is similar to the algebra in the Killing horizon case, but with a modification that agrees with other approaches to universal horizon thermodynamics.