Horava gravity vs. thermodynamics: the black hole case

TL;DR

This paper investigates black hole solutions in Horava gravity, revealing the existence of universal horizons that could resolve thermodynamic paradoxes related to Lorentz invariance violation and causality issues.

Contribution

It demonstrates the presence of universal horizons in Horava gravity and analyzes their stability, providing insights into black hole thermodynamics in Lorentz-violating theories.

Findings

Universal horizons exist in spherical symmetry in Horava gravity.

Aspherical perturbations destabilize the universal horizon, leading to singularities.

Black holes lack non-standard long-range hair.

Abstract

Under broad assumptions breaking of Lorentz invariance in gravitational theories leads to tension with unitarity because it allows for processes that apparently violate the second law of thermodynamics. The crucial ingredient of this argument is the existence of black hole solutions with the interior shielded from infinity by a causal horizon. We study how the paradox can be resolved in the healthy extension of Horava gravity. To this aim we analyze classical solutions describing large black holes in this theory with the emphasis on their causal structure. The notion of causality is subtle in this theory due to the presence of instantaneous interactions. Despite this fact, we find that within exact spherical symmetry a black hole solution contains a space-time region causally disconnected from infinity by a surface of finite area -- the `universal horizon'. We then consider small perturbations of arbitrary angular dependence in the black hole background. We argue that aspherical perturbations destabilize the universal horizon and, at non-linear level, turn it into a finite-area singularity. The causal structure of the region outside the singularity is trivial. If the higher-derivative terms in the equations of motion smear the singularity while preserving the trivial causal structure of the solutions, the thermodynamics paradox would be obviated. As a byproduct of our analysis we prove that the black holes do not have any non-standard long-range hair. We also comment on the relation with Einstein-aether theory, where the solutions with universal horizon appear to be stable.