Can Extremal Black Holes Have Non-Zero Entropy ?

TL;DR

This paper examines whether extremal black holes can have non-zero entropy by reviewing various theoretical perspectives, highlighting conflicting evidence from classical and string theory approaches, and attempting to reconcile these differences.

Contribution

It provides a comprehensive review of arguments regarding extremal black hole entropy and explores potential ways to reconcile classical and quantum perspectives.

Findings

Extremal black holes cannot be obtained as limits of non-extremal black holes.

Classical arguments suggest extremal black holes have zero entropy.

String theory calculations indicate extremal black holes obey the area law for entropy.

Abstract

We give several pieces of evidence to show that extremal black holes cannot be obtained as limits of non-extremal black holes. We review arguments in the literature showing that the entropy of extremal black holes is zero, while that of near-extremal ones obey the Bekenstein-Hawking formula. However, from the counting of degeneracy of quantum (BPS) states of string theory the entropy of extremal stringy black holes obeys the area law. An attempt is made to reconcile these arguments.