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 requiresthat the areas of the outermost trapped surfaces are preserved. We argue that the condition that the area of the eventhorizon should not decrease is necessary –but not sufficient– for the semirigidity assumption to hold. It is known thatthe 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. Recentstudies on the interactions of black holes with fermionic fields imply a generic formation of naked singularities. Thepresence of these singularities invalidates the laws of black hole dynamics and the cosmic censorship conjecture for theprocesses that satisfy the weak energy condition.