Abstract
Black holes in Lorentz-violating theories have been claimed to violate the second law of thermodynamics by perpetual motion energy extraction. We revisit this question for a Penrose splitting process in a spherically symmetric setting with two species of particles that move on radial geodesics that extend to infinity. We show that energy extraction by this process cannot happen in any theory in which gravity is attractive, in the sense of a geometric inequality that we describe. This inequality is satisfied by all known Einstein-\ae{}ther and Ho\v{r}ava black hole solutions.
Highlights
The defining property of a black hole is that nothing can escape from its interior which, in general relativity, is separated from the exterior by a null hypersurface called the event horizon
Black holes in Lorentz-violating theories have been claimed to violate the second law of thermodynamics by perpetual motion energy extraction
We revisit this question for a Penrose splitting process in a spherically symmetric setting with two species of particles that move on radial geodesics that extend to infinity
Summary
The defining property of a black hole is that nothing can escape from its interior which, in general relativity, is separated from the exterior by a null hypersurface called the event horizon. Each excitation could keep a linear dispersion relation but with differing propagation speeds In this case different massless excitations propagate along the null cones of distinct effective metrics. This second scenario should still capture some aspects of the low-momentum behaviour present in the first scenario. Our results do not directly contest the perpetuum mobile constructions of [17,18] They do indicate that removing the external agents from the construction and considering dynamics introduces a significant new obstruction. We view this result as a strong and qualitatively new argument against violation of the generalized second law in Lorentz-violating gravitational theories.
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