Entropy of an extremal regular black hole

TL;DR

This paper studies a magnetically charged extremal regular black hole in Einstein gravity coupled with nonlinear electrodynamics, revealing that the entropy function approach fails to produce the correct Bekenstein-Hawking entropy due to nonlinearity.

Contribution

It introduces a new extremal regular black hole model and analyzes the limitations of the entropy function approach in this context.

Findings

Entropy function approach does not yield correct entropy for the regular black hole.

Contrasts with the extremal Reissner-Nordström black hole case.

Nonlinearity of the entropy function causes the failure.

Abstract

We introduce a magnetically charged extremal regular black hole in the coupled system of Einstein gravity and nonlinear electrodynamics. Its near horizon geometry is given by $AdS_2\times S^2$. It turns out that the entropy function approach does not automatically lead to a correct entropy of the Bekenstein-Hawking entropy. This contrasts to the case of the extremal Reissner-Norstr\"om black hole in the Einstein-Maxwell theory. We conclude that the entropy function approach does not work for a magnetically charged extremal regular black hole without singularity, because of the nonlinearity of the entropy function.