On the third law of black hole dynamics

TL;DR

This paper explores the third law of black hole dynamics, showing that the surface gravity and gravitational charge cannot reach zero through finite processes, with implications for extremal black holes.

Contribution

It extends the third law to gravitational charge and analyzes the behavior of infalling energy near extremality in black holes.

Findings

Surface gravity cannot be reduced to zero in finite steps.

Gravitational charge behaves similarly to surface gravity near extremality.

Infalling energy and radiation are constrained as extremality is approached.

Abstract

The third law of black hole dynamics states that the surface gravity (temperature) of black hole cannot be reduced to zero in finite sequence of physical interactions. We argue that the same is true when surface gravity is replaced by gravitational charge. We demonstrate that the prescribed window for infalling energy and radiation pinches off as extremality ($M^2 = a^2 + Q^2 $) is approached.