Black Hole Evaporation in Ho\v{r}ava-Lifshitz Gravity

Ho\v{r}ava-Lifshitz (HL) gravity was formulated in hope of solving the non-renormalization problem in Einstein gravity and the ghost problem in higher derivative gravity theories by violating Lorentz invariance. In this work we consider the spherically symmetric neutral AdS black hole evaporation process in HL gravity in various spacetime dimensions $d$, and with detailed balance violation parameter $0\leqslant \epsilon^2\leqslant 1$. We find that the lifetime of the black holes under Hawking evaporation is dimensional dependent, with $d=4,5$ behave differently from $d\geqslant 6$. For the case of $\epsilon=0$, in $d=4,5$, the black hole admits zero temperature state, and the lifetime of the black hole is always infinite. This phenomenon obeys the third law of black hole thermodynamics, and implies that the black holes become an effective remnant towards the end of the evaporation. As $d\geqslant 6$, however, the lifetime of black hole does not diverge with any initial black hole mass, and it is bounded by a time of the order of $\ell^{d-1}$, similar to the case of Schwarzschild-AdS in Einstein gravity (which corresponds to $\epsilon^2=1$), though for the latter this holds for all $d\geqslant 4$. The case of $0<\epsilon^2<1$ is also qualitatively similar with $\epsilon=0$.