Evaporation and Fate of Dilatonic Black Holes

Abstract

We study both spherically symmetric and rotating black holes with dilaton coupling and discuss the evaporation of these black holes via Hawking&#39;s quantum radiation and their fates. We find that the dilaton coupling constant $α$ drastically affects the emission rates, and therefore the fates of the black holes. When the charge is conserved, the emission rate from the non-rotating hole is drastically changed beyond $α= 1$ (a superstring theory) and diverges in the extreme limit. In the rotating cases, we analyze the slowly rotating black hole solution with arbitrary $α$ as well as three exact solutions, the Kerr--Newman ($α= 0$), and Kaluza--Klein ($α= \sqrt{3}$), and Sen black hole ($α= 1$ and with axion field). Beyond the same critical value of $α\sim 1$, the emission rate becomes very large near the maximally charged limit, while for $α<1$ it remains finite. The black hole with $α> 1$ may evolve into a naked singularity due to its large emission rate. We also consider the effects of a discharge process by investigating superradiance for the non-rotating dilatonic black hole.