Black hole radiation in the presence of a universal horizon

In Ho\v{r}ava and Einstein-{\AE}ther theories of modified gravity, in spite of the violation of Lorentz invariance, spherically-symmetric stationary black hole solutions possess an inner universal horizon which separates field configurations into two disconnected classes. We compute the late time radiation emitted by a dispersive field propagating in such backgrounds. We fix the initial conditions on stationary modes by considering a regular collapsing geometry, and imposing that the state inside the infalling shell is vacuum. We find that the mode pasting across the shell is adiabatic at late time (large inside frequencies). This implies that large black holes emit a thermal flux with a temperature fixed by the surface gravity of the Killing horizon. In turn, this suggests that the universal horizon should play no role in the thermodynamical properties of these black holes.