Ray tracing Einstein-Æther black holes: Universal versus Killing horizons

Abstract

Violating Lorentz invariance, and so implicitly permitting some form of super-luminal communication, necessarily alters the notion of a black hole. Nevertheless, in both Einstein-\ae{}ther gravity and Ho\ifmmode \check{r}\else \v{r}\fi{}ava-Lifshitz gravity, there is still a causally disconnected region in black-hole solutions, now being bounded by a ``universal horizon,'' which traps excitations of arbitrarily high velocities. To better understand the nature of these black holes, and their universal horizons, we study ray trajectories in these spacetimes. We find evidence that Hawking radiation is associated with the universal horizon, while the ``lingering'' of ray trajectories near the Killing horizon hints at reprocessing there. In doing this we solve an apparent discrepancy between the surface gravity of the universal horizon and the associated temperature derived by the tunneling method. These results advance the understanding of these exotic horizons and provide hints for a full understanding of black-hole thermodynamics in Lorentz-violating theories.