Dilaton black holes in grand canonical ensemble near the extreme state

TL;DR

This paper investigates the thermodynamic properties of electrically charged dilaton black holes in a grand canonical ensemble near extremality, revealing conditions under which the temperature approaches zero while entropy remains finite.

Contribution

It demonstrates the existence of boundary conditions where the Hawking temperature vanishes at infinite horizon radius with finite, non-zero entropy in dilaton black holes.

Findings

Hawking temperature can smoothly approach zero near extremality.

Horizon area and entropy remain finite and non-zero.

Existence of a horizon in the extremal limit is due to system finiteness in string theory.

Abstract

Dilaton black holes with a pure electric charge are considered in a framework of a grand canonical ensemble near the extreme state. It is shown that there exists such a subset of boundary data that the Hawking temperature smoothly goes to zero to an infinite value of a horizon radius but the horizon area and entropy are finite and differ from zero. In string theory the existence of a horizon in the extreme limit is due to the finiteness of a system only.