Test fields cannot destroy extremal black holes

TL;DR

This paper proves that test fields satisfying the null energy condition cannot violate the weak cosmic censorship conjecture by destroying extremal Kerr-Newman or Kerr-Newman-AdS black holes, supporting their stability.

Contribution

It demonstrates, using thermodynamics, that extremal black holes cannot be overspun or overcharged by test fields, without assuming cosmic censorship.

Findings

Test fields satisfying the null energy condition cannot destroy extremal black holes.

The proof relies on black hole thermodynamics and is independent of field specifics.

Results extend to other extremal black hole solutions.

Abstract

We prove that (possibly charged) test fields satisfying the null energy condition at the event horizon cannot overspin/overcharge extremal Kerr-Newman or Kerr-Newman-anti de Sitter black holes, that is, the weak cosmic censorship conjecture cannot be violated in the test field approximation. The argument relies on black hole thermodynamics (without assuming cosmic censorship), and does not depend on the precise nature of the fields. We also discuss generalizations of this result to other extremal black holes.