Spontaneous breaking of Lorentz invariance, black holes and perpetuum mobile of the 2nd kind

TL;DR

This paper explores how spontaneous Lorentz invariance breaking, via ghost condensate, alters black hole thermodynamics, leading to non-universal temperatures and potential violations of the second law of thermodynamics.

Contribution

It demonstrates that Lorentz symmetry breaking causes black hole temperature to depend on particle species, challenging the universality of black hole thermodynamics.

Findings

Black hole temperature varies with particle maximal velocities.

Lorentz breaking leads to violation of the second law of thermodynamics.

Potential construction of a perpetuum mobile of the second kind.

Abstract

We study the effect of spontaneous breaking of Lorentz invariance on black hole thermodynamics. We consider a scenario where Lorentz symmetry breaking manifests itself by the difference of maximal velocities attainable by particles of different species in a preferred reference frame. The Lorentz breaking sector is represented by the ghost condensate. We find that the notions of black hole entropy and temperature loose their universal meaning. In particular, the standard derivation of the Hawking radiation yields that a black hole does emit thermal radiation in any given particle species, but with temperature depending on the maximal attainable velocity of this species. We demonstrate that this property implies violation of the second law of thermodynamics, and hence, allows construction of a perpetuum mobile of the 2nd kind. We discuss possible interpretation of these results.