Black Holes and the Third Law of Thermodynamics

TL;DR

This paper examines the third law of thermodynamics in black hole physics, discussing the unattainability principle, zero temperature limits, and entropy behavior of extremal black holes, highlighting potential violations and their implications.

Contribution

It provides a detailed analysis of the third law in black hole thermodynamics, proposing that extremal black holes may have zero entropy, challenging the Bekenstein-Hawking law.

Findings

Zero entropy for extremal black holes as a natural solution.

Potential violation of the second law in charged black holes.

Discontinuity between extremal and non-extremal states supported.

Abstract

We discuss in the framework of black hole thermodynamics some aspects relative to the third law in the case of black holes of the Kerr-Newman family. In the light of the standard proof of the equivalence between the unattainability of the zero temperature and the entropic version of the third law it is remarked that the unattainability has a special character in black hole thermodynamics. Also the zero temperature limit which obtained in the case of very massive black holes is discussed and it is shown that a violation of the entropic version in the charged case occurs. The violation of the Bekenstein-Hawking law in favour of zero entropy S_E=0 in the case of extremal black holes is suggested as a natural solution for a possible violation of the second law of thermodynamics. Thermostatic arguments in support of the unattainability are explored, and $S_E=0$ for extremal black holes is shown to be again a viable solution. The third law of black hole dynamics by W.Israel is then interpreted as a further strong corroboration to the picture of a discontinuity between extremal states and non-extremal ones.