Abstract

Recently it has been shown that the third law of black hole mechanics can be violated: an exactly extremal Reissner-Nordström black hole can form in finite time in gravitational collapse of matter with a large charge to mass ratio. However, it has also been proved that this cannot happen if the matter satisfies a “supersymmetric” lower bound on its energy in terms of its charge. In this talk, I will discuss these developments, as well as extensions of this latter proof to supersymmetric black holes with a negative cosmological constant and for such black holes (with non-positive cosmological constant) not formed in collapse. The proofs of these results rely on ideas related to quasi-local energy and proofs of the positive energy theorems: these shall be discussed, and the main theorem given as a rigidity result associated with the interior of a “supersymmetric surface” – a concept to be introduced.