Thermodynamic properties of massive dilaton black holes II

We numerically reanalyze static and spherically symmetric black hole solutions in an Einstein-Maxwell-dilaton system with a dilaton potential $m_d^2{\varphi }^2$. We investigate thermodynamic properties for various dilaton coupling constants and find that thermodynamic properties change at a critical dilaton mass $m_{d,crit}$. For $m_d\ge m_{d,crit}$, the black hole becomes an extreme solution for a nonzero horizon radius $r_{h,ex}$ as the Reissner-Nordstr"om black hole. However, if $m_d$ is nearly equal to $m_{d,crit}$, there appears a solution of smaller horizon radius than $r_{h,ex}$. For $m_d<m_{d,crit}$, a solution continues to exist until the horizon approaches zero. The Hawking temperature in the zero horizon limit resembles that of a massless dilaton black hole for arbitrary dilaton coupling constant.