Mechanics of universal horizons

TL;DR

This paper explores the properties of universal horizons in modified gravity theories like Einstein-{ {a}}ther theory, establishing black hole thermodynamics and suggesting potential extensions of holography despite Lorentz invariance violation.

Contribution

It derives a Smarr formula and first law for universal horizons and constructs new analytic solutions, advancing understanding of black holes in Lorentz-violating gravity models.

Findings

Universal horizons act as causal boundaries in these theories.

A Smarr formula for universal horizons is established.

The first law of black hole mechanics is adapted for universal horizons.

Abstract

Modified gravity models such as Ho\v{r}ava-Lifshitz gravity or Einstein-{\ae}ther theory violate local Lorentz invariance and therefore destroy the notion of a universal light cone. Despite this, in the infrared limit both models above possess static, spherically symmetric solutions with "universal horizons" - hypersurfaces that are causal boundaries between an interior region and asymptotic spatial infinity. In other words, there still exist black hole solutions. We construct a Smarr formula (the relationship between the total energy of the spacetime and the area of the horizon) for such a horizon in Einstein-{\ae}ther theory. We further show that a slightly modified first law of black hole mechanics still holds with the relevant area now a cross-section of the universal horizon. We construct new analytic solutions for certain Einstein-{\ae}ther Lagrangians and illustrate how our results work in these exact cases. Our results suggest that holography may be extended to these theories despite the very different causal structure as long as the universal horizon remains the unique causal boundary when matter fields are added.