Lorentz violation and perpetual motion

TL;DR

This paper demonstrates that theories violating Lorentz invariance with multiple propagation speeds conflict with black hole thermodynamics, challenging the possibility of perpetual motion machines in such frameworks.

Contribution

It extends previous results by showing that Lorentz violation with multiple speeds conflicts with the generalized second law, even without assuming specific interactions beyond gravity.

Findings

Lorentz violating theories with multiple speeds violate black hole entropy laws

Classical energy extraction analogous to Penrose process can decrease black hole entropy

Large black holes can avoid instabilities that threaten perpetual motion

Abstract

We show that any Lorentz violating theory with two or more propagation speeds is in conflict with the generalized second law of black hole thermodynamics. We do this by identifying a classical energy-extraction method, analogous to the Penrose process, which would decrease the black hole entropy. Although the usual definitions of black hole entropy are ambiguous in this context, we require only very mild assumptions about its dependence on the mass. This extends the result found by Dubovsky and Sibiryakov, which uses the Hawking effect and applies only if the fields with different propagation speeds interact just through gravity. We also point out instabilities that could interfere with their black hole {\it perpetuum mobile}, but argue that these can be neglected if the black hole mass is sufficiently large.