# Cosmic censorship and the third law of black hole dynamics

## TL;DR

This paper critiques the assumptions behind Israel's proof of the third law of black hole dynamics, highlighting the necessity of cosmic censorship and the potential formation of naked singularities that challenge existing laws.

## Contribution

It argues that the current proof relies on unverified assumptions and that recent findings suggest naked singularities can form, undermining the validity of the third law and cosmic censorship.

## Key findings

- Presence of naked singularities can invalidate black hole laws
- Weak energy condition does not prevent naked singularity formation
- Current proofs of the third law are incomplete

## Abstract

Israel's proof of the third law of black hole dynamics is based on the semi-rigidity assumption which requires that the areas of the outermost trapped surfaces are preserved. We argue that the condition that the area of the event horizon should not decrease is necessary -but not sufficient- for the semi-rigidity assumption to hold. It is known that the presence of a naked singularity in the exterior region invalidates Hawking's proof of the area theorem. In this sense, the third law assumes the validity of the strong form of the cosmic censorship conjecture, contrary to general acceptance. Still, one cannot guarantee that the semi-rigidity assumption holds. Therefore the current proof is incomplete. Recent studies on the interactions of black holes with fermionic fields imply a generic formation of naked singularities. The presence of these singularities invalidates the laws of black hole dynamics and cosmic censorship conjecture for the processes that satisfy the weak energy condition.