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

TL;DR

The paper investigates how spontaneous Lorentz symmetry breaking, implemented via a ghost-condensate sector, alters black hole thermodynamics. By deriving a species-dependent Hawking temperature $T_ψ = T_H /(1+\varepsilon)^{3/2} = v^3 T_H$ and showing that different fields perceive different horizons, it questions the universality of black hole entropy and temperature. It then presents a thought experiment where energy is transferred between shells coupled to distinct species, potentially violating the second law, and discusses several possible interpretations and UV-completion requirements. The work suggests that Lorentz-violating IR modifications can fundamentally challenge standard black hole thermodynamics and provide constraints on the viability of such theories in a complete quantum gravity framework.

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.