Fermionic greybody factors in dilaton black holes

TL;DR

This paper investigates fermion emission from dilaton black holes, calculating greybody factors for various couplings, and analyzes how these influence the black hole's evaporation or stability, revealing a transition between decay and extremal regimes.

Contribution

It provides both numerical and analytical calculations of greybody factors for fermions in dilaton black holes across different coupling constants, and explores the black hole's final fate considering backreaction effects.

Findings

Greybody factors depend on the dilaton coupling constant.

A transition line separates decay and extremal regimes.

Black holes either evaporate completely or stabilize at extremality.

Abstract

In this paper the question of emission of fermions in the process of dilaton black hole evolution and its characters for different dilaton coupling constants $\alpha$ is studied. The main quantity of interest, the greybody factors are calculated both numerically and in analytical approximation. The dependence of rates of evaporation and behaviour on the dilaton coupling constant is analyzed. Having calculated the greybody factors we are able to address the question of the final fate of the dilaton black hole. For that we also need to make dynamical treatment of the solution by considering the backreaction which will show a crucial effect on the final result. We find a transition line in $(Q/M, \alpha)$ plane that separates the two regimes for the fate of the black hole, decay regime and extremal regime. In the decay regime the black hole completely evaporates, while in the extremal regime the black hole approaches the extremal limit by radiation and becomes stable.