Entropy of extreme three-dimensional charged black holes

TL;DR

This paper demonstrates that three-dimensional charged black holes can reach an extreme state at nonzero temperature and that their entropy is consistently described by the Bekenstein-Hawking formula, regardless of the treatment method.

Contribution

It shows the entropy of extreme three-dimensional charged black holes is uniquely given by the Bekenstein-Hawking formula, contrasting with even-dimensional cases.

Findings

Extreme three-dimensional charged black holes can have nonzero temperature.

The entropy is consistently described by the Bekenstein-Hawking formula.

Different treatments of black hole preparation yield the same entropy result.

Abstract

It is shown that three-dimensional charged black holes can approach the extreme state at nonzero temperature. Unlike even dimensional cases, the entropy for the extreme three-dimensional charged black hole is uniquely described by the Bekenstein-Hawking formula, regardless of different treatments of preparing the extreme black hole, namely, Hawking's treatment and Zaslavskii's treatment.