Does the third law of black hole thermodynamics really have a serious failure?

TL;DR

This paper examines the apparent failure of the third law of black hole thermodynamics, highlighting the fundamental differences between extremal and non-extremal black holes and suggesting the need for a revised formulation of the law.

Contribution

It provides insights into the distinctions between extremal and non-extremal black holes, questioning the conventional third law and proposing a direction for a more consistent thermodynamic framework.

Findings

Extremal and non-extremal black holes are fundamentally different.

The boundary between extremal and non-extremal black holes is very thin.

A careful reformulation of the third law may resolve existing issues.

Abstract

The almost perfect correspondence between certain laws of classical black hole mechanics and the ordinary laws of thermodynamics is spoiled by the failure of the conventional back hole analogue of the third law. Our aim here is to contribute to the associated discussion by flashing light on some simple facts of black hole physics. However, no attempt is made to lay to rest the corresponding long lasting debate. Instead, merely some evidence is provided to make it clear that although the borderline between extremal and non-extremal black holes is very thin they are essentially different. Hopefully, a careful investigation of the related issues will end up with an appropriate form of the third law and hence with an unblemished setting of black hole thermodynamics.