Algebra of Universal Horizon Preserving Diffeomorphisms

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.