Entropy of extremal black holes from entropy of quasiblack holes

TL;DR

This paper derives the entropy of extremal black holes from quasiblack holes, showing it can vary continuously and is not necessarily equal to the Bekenstein-Hawking entropy, challenging traditional assumptions.

Contribution

It introduces a continuity approach from quasiblack holes to extremal black holes, demonstrating the entropy can be any non-negative value, not fixed at A/4.

Findings

Extremal black hole entropy can vary continuously from quasiblack holes.

The entropy of extremal black holes is not necessarily equal to A/4.

A zero entropy with non-zero temperature at infinity is physically unsatisfactory.

Abstract

The entropy of extremal black holes (BHs) is obtained using a continuity argument from extremal quasiblack holes (QBHs). It is shown that there exists a smooth limiting transition in which (i) the system boundary approaches the extremal Reissner-Nordstr\"{o}m (RN) horizon, (ii) the temperature at infinity tends to zero and quantum backreaction remains bounded on the horizon, and (iii) the first law of thermodynamics is satisfied.The conclusion is that the entropy $S$ of extremal QBHs and of extremal BHs can take any non-negative value, only in particular cases it coincides with $ S=A/4$. The choice $S=0$ with non-zero temperature at infinity is rejected as physically unsatisfactory