Dynamical obstruction to perpetual motion from Lorentz-violating black holes

Understand

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.