Weak Energy Condition, Trapped Surfaces and Black hole Third Law

TL;DR

This paper examines the third law of thermodynamics in dynamical Vaidya black holes across multiple dimensions, analyzing the consistency of various definitions of surface gravity and extremality under the weak energy condition.

Contribution

It demonstrates the consistency of different surface gravity and extremality definitions for Vaidya black holes and explores the implications of the weak energy condition on their evolution.

Findings

Definitions of surface gravity are consistent for the considered black holes.

Under the weak energy condition, non-extremal black holes can evolve to extremality.

Potential conflicts between assumptions are identified in certain parameter ranges.

Abstract

We consider the third law of thermodynamics for families of 4- and n-dimensional Vaidya black holes, including many of interest. Since there are several versions of the definition of surface gravity as well as the extremality condition for dynamical black holes, we first show that for the considered 4- and n-dimensional Vaidya families, these definitions are consistent with each other. We assume, first, that a non-extremal black hole evolves to an extremality state after a finite time and second, that the weak energy condition for the source holds at all times. We then compare the results of these assumptions and investigate whether there are ranges of black hole parameters where these two assumptions are in conflict.