Lorentz violation and perpetual motion

TL;DR

The paper analyzes Lorentz-violating theories with multiple propagation speeds, where nested black hole horizons have distinct temperatures, challenging the generalized second law (GSL) of black hole thermodynamics. It extends Dubovsky and Sibiryakov by showing that a classical Penrose-like energy-extraction process can reduce the black hole mass by a factor proportional to $M$ within a time $\\mathcal{O}(R)$, without external entropy production, implying GSL violation under mild assumptions on $S_{ m bh}(M)$. The authors also examine destabilizing channels such as gravitational equilibration and ergoregion instabilities and argue that these can be suppressed for sufficiently large black holes, leaving the GSL-violating mechanism robust; moreover, the violation persists even if $A$ and $B$ interact directly. A potential resolution is that the UV completion eliminates the causally hidden region, in which case the GSL reduces to the ordinary second law; otherwise, the results suggest a deep tie between black hole thermodynamics and Lorentz symmetry.

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.

Figures (1)

• Figure 1: The radial 4-momentum covector space at the point $x$ in the ergoregion ($p_a m^a=0$ for all vectors $m^a$ tangent to the symmetry sphere through $x$). The momenta with vanishing Killing energy ${\cal E}=p_a\xi^a$ lie along the dashed line. ${\cal E}$ is negative for $p_A$, since $x$ lies in the $A$ ergoregion, while it is positive for all momenta on the $B$ null cone. The total 4-momentum $P$ has positive ${\cal E}$, hence it points above the dashed line.