# An improved derivation of the Smarr Formula for Lorentz-breaking gravity

## TL;DR

This paper introduces a new method to derive the Smarr formula for Lorentz-breaking gravity theories, extending previous static results to rotating black holes and exploring thermodynamics of universal horizons.

## Contribution

It presents a novel, scale invariance-based approach to derive the Smarr formula for Einstein-Aether and Horava gravity, including rotating black holes with universal horizons.

## Key findings

- Derived Smarr formulae for stationary rotating black holes in Lorentz-breaking gravity.
- Extended thermodynamic analysis to three-dimensional black holes with universal horizons.
- Confirmed the viability of black hole thermodynamics in Lorentz-violating theories.

## Abstract

Thermodynamical properties of black holes in gravitational theories without Local Lorentz invariance have been subject to intense investigation in the past years due to the presence of universal horizons, which are strong causal barriers even for superluminal signals. Here we present a novel general method for deriving the Smarr formula for this class of theories: in particular we show that the Smarr formulae for Einstein-Aether theory and infrared Horava gravity follow from scale invariance. We not only reproduce straightforwardly previous findings for static black hole solutions, but we are also able to generalise them to the case of stationary rotating black holes. Finally, we apply our results to the rotating black holes with universal horizon as found in three dimensions, from which we shall draw some lessons on the viability of black hole thermodynamics for black hole solutions endowed with universal horizons.