On the first law of black holes with a universal horizon

TL;DR

This paper investigates whether universal horizons in Lorentz-violating gravity theories obey laws similar to black hole thermodynamics, finding that simple interpretations are problematic and highlighting the need for further study.

Contribution

It analyzes the applicability of the first law of black hole mechanics to universal horizons, revealing challenges in their thermodynamical interpretation.

Findings

Universal horizons do not straightforwardly satisfy the first law.

Simple thermodynamical interpretations are problematic for these horizons.

Further systematic study of rotating universal horizons is needed.

Abstract

In Lorentz violating theories of gravitation with a preferred foliation a notion of black hole is still possible, despite the presence of infinitely fast propagating modes. Such event horizons are known as universal horizons. Their discovery poses the question of whether they satisfy mechanical laws, analogous to the ones of Killing horizons in Lorentz symmetric theories, and whether they admit a thermodynamical interpretation. In this paper we study the viability of the first law for several exact universal horizon solutions previously derived in the literature. Our results show that a simple mechanical and thermodynamical interpretation is problematic in these cases, and call for a more systematic study of rotating universal horizons.