Evaporation and Fate of Dilatonic Black Holes

TL;DR

This paper investigates how the dilaton coupling constant affects the evaporation and ultimate fate of both non-rotating and rotating black holes, revealing critical behavior at $ ext{alpha} ext{~} 1$ and potential evolution into naked singularities.

Contribution

It provides a detailed analysis of evaporation rates for dilatonic black holes across different coupling constants and solutions, highlighting critical thresholds and their implications.

Findings

Emission rates diverge for $ ext{alpha} > 1$ in extreme limits.

Black holes with $ ext{alpha} > 1$ may evolve into naked singularities.

Superradiance effects influence discharge processes 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's quantum radiation and their fates. We find that the dilaton coupling constant $\alpha$ 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 $\alpha = 1$ (a superstring theory) and diverges in the extreme limit. In the rotating cases, we analyze the slowly rotating black hole solution with arbitrary $\alpha$ as well as three exact solutions, the Kerr--Newman ($\alpha = 0$), and Kaluza--Klein ($\alpha = \sqrt{3}$), and Sen black hole ($\alpha = 1$ and with axion field). Beyond the same critical value of $\alpha \sim 1$, the emission rate becomes very large near the maximally charged limit, while for $\alpha<1$ it remains finite. The black hole with $\alpha > 1$ 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.