Universal horizons in maximally symmetric spaces

Abstract

Universal horizons in Hořava–Lifshitz gravity and Einstein-æther 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 (IR) 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 Hořava–Lifshitz gravity with a universal horizon is also a solution of Einstein-æther theory, thereby broadening and complementing the known equivalence region of the solution spaces.