Cosmic censorship and the third law of black hole dynamics

Abstract

Israel's proof of the third law of black hole dynamics is based on the semirigidity 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 semirigidity 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 semirigidity 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 the cosmic censorship conjecture for the processes that satisfy the weak energy condition.