Entropy of extremal black holes in asymptotically anti-de Sitter spacetime

TL;DR

This paper explores the entropy characteristics of extremal black holes in anti-de Sitter spacetime, revealing that the order of extremalization and quantization affects the entropy calculation, with implications for black hole thermodynamics.

Contribution

It clarifies how the sequence of extremalization and quantization influences the entropy of extremal black holes in anti-de Sitter spacetime, contrasting with previous results in ordinary spacetime.

Findings

Extremal black holes in AdS spacetime can have zero entropy if quantization follows extremalization.

If quantization occurs before extremalization, the entropy matches the Bekenstein-Hawking area law.

The order of operations significantly impacts the thermodynamic properties of black holes in AdS spacetime.

Abstract

Unlike the extremal Reissner - Nordstr\"{o}m black hole in ordinary spacetime, the one in anti-de Sitter spacetime is a minimum of action and has zero entropy if quantization is carried out after extremalization. However, if extremalization is carried out after quantization, then the entropy is a quarter of the area as in the usual case.