A possible explanation of the clash for black hole entropy in the extremal limit

TL;DR

This paper investigates the discrepancy in extremal black hole entropy depending on the order of limits taken, analyzing classical and quantum entropy through different procedures and proposing a quantum effect-based explanation.

Contribution

It introduces a detailed analysis of the extremal black hole entropy clash by examining classical and quantum effects with different limit procedures.

Findings

Classical entropy depends on the order of taking limits.

Quantum scalar field entropy varies with limit procedures.

A quantum effect-based explanation for the entropy clash is proposed.

Abstract

It is shown that the classical entropy of the extremal black hole depends on two different limits procedures. If we first take the extremal limit and then the boundary limit, the entropy is zero; if we do it the other way round, we get the Bekenstein-Hawking entropy. By means of the brick wall model, the quantum entropy of scalar field in the extremal black hole background has been calculated for the above two different limits procedures. A possible explanation which considers the quantum effect for the clash of black hole entropy in the extremal limit is given.