Universal horizons in maximally symmetric spaces

TL;DR

This paper classifies all static, spherically symmetric universal horizons in maximally symmetric spaces within Hořava-Lifshitz gravity and Einstein-{ extquoteright}aether theory, deriving their thermodynamics and demonstrating their equivalence.

Contribution

It provides a complete classification of universal horizon solutions with asymptotic charges and first laws, and shows their equivalence across theories.

Findings

Complete classification of universal horizons in maximally symmetric spaces.

Derivation of first laws for these horizons.

Proof of solution equivalence between Hořava-Lifshitz gravity and Einstein-{ extquoteright}aether theory.

Abstract

Universal horizons in Ho\v{r}ava-Lifshitz gravity and Einstein-{\ae}ther theory are the equivalent of causal horizons in general relativity and appear to have many of the same properties, including a first law of horizon thermodynamics and thermal radiation. Since universal horizons are infrared solutions of a putative power counting renormalizable quantum gravitational theory, fully understanding their thermodynamics will shed light on the interplay between black hole thermodynamics and quantum gravity. In this paper, we provide a complete classification, including asymptotic charges, of all four dimensional static and spherically symmetric universal horizon solutions with maximally symmetric asymptotics -- the equivalents of the Schwarzschild, Schwarzschild de Sitter or Schwarzschild anti-de Sitter spacetimes. Additionally we derive the associated first laws for the universal horizon solutions. Finally we prove that independent of asymptotic boundary conditions, any spherically symmetric solution in Ho\v{r}ava-Lifshitz gravity with a universal horizon is also a solution of Einstein-{\ae}ther theory, thereby broadening and complementing the known equivalence region of the solution spaces.