Action and Entropy of Extreme and Non-Extreme Black Holes

TL;DR

This paper compares the Hamiltonian actions of extreme and non-extreme black holes, explaining why extreme black holes lack entropy due to absent horizon degrees of freedom, unlike their non-extreme counterparts.

Contribution

It provides a simple derivation showing the absence of entropy in extreme black holes by contrasting their Hamiltonian actions with non-extreme black holes.

Findings

Non-extreme black holes have horizon degrees of freedom that contribute to entropy.

Extreme black holes lack these horizon degrees of freedom and thus have no entropy.

The paper offers a straightforward derivation of the entropy difference.

Abstract

The Hamiltonian actions for extreme and non-extreme black holes are compared and contrasted and a simple derivation of the lack of entropy of extreme black holes is given. In the non-extreme case the wave function of the black hole depends on horizon degrees of freedom which give rise to the entropy. Those additional degrees of freedom are absent in the extreme case.