Spontaneous Lorentz Violation, Negative Energy and the Second Law of Thermodynamics

TL;DR

This paper demonstrates that theories with spontaneous Lorentz violation can lead to violations of the generalized second law of thermodynamics through negative energy flow into black holes, highlighting potential fundamental issues with such theories.

Contribution

It provides explicit solutions showing second law violations via negative energy flow in Lorentz-violating theories, independent of additional couplings or assumptions.

Findings

Existence of solutions with negative energy flow into black holes.

Violation of the second law of thermodynamics in Lorentz-violating theories.

Null energy condition violation as a potential source of theoretical pathology.

Abstract

We reconsider the possibility of violating the generalized second law of thermodynamics in theories with spontaneous Lorentz violation. It has been proposed that this may be accomplished in particular with a black hole immersed in a ghost condensate background, which may be taken to break Lorentz invariance without appreciably distorting the space-time geometry. In this paper we show that there in fact exist solutions explicitly describing flow of negative energy into these black holes, allowing for violation of the second law in a very simple way. This second law violation is independent of any additional assumptions such as couplings of the ghost condensate to secondary fields, and suggests that violation of the null energy condition may be the true source of pathology in these theories.