Thermodynamic properties of massive dilaton black holes

Abstract

We numerically reanalyze static and spherically symmetric black hole solutions in an Einstein-Maxwell-dilaton system with a dilaton potential. We consider two types of potentials: ${m}_{d}^{2}{\ensuremath{\varphi}}^{2}$ and ${m}_{d}^{2}{S}^{2}(S\ensuremath{-}{1)}^{2}{e}^{S\ensuremath{-}1}/4$ where $S\ensuremath{\mathrel{:=}}{e}^{\ensuremath{-}2\ensuremath{\varphi}},$ which is proposed based on gluino condensation. We investigate thermodynamic properties in both cases and find that the black hole becomes an extreme solution for a finite horizon radius when a dilaton potential does not vanish. As a result, the Hawking temperature approaches zero in the extreme limit whereas it approaches a finite nonzero value in this limit for the massless dilaton case. This implies that a small amount of the dilaton mass changes the final fate of the black hole.