  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.
