Abstract

The third law of black hole mechanics asserts that it is impossible for a non-extremal black hole to become extremal in finite time (in classical General Relativity). A proof of this law was claimed in the 1980s. However, counterexamples to this law were found recently: gravitational collapse of a massless charged scalar field can produce an exactly extremal Reissner-Nordstrom black hole in finite time, passing through an intermediate phase in which the solution is exactly Schwarzschild at the horizon. These examples involve matter with a large charge to mass ratio. What about theories, such as supersymmetric theories, with an upper bound on the charge to mass ratio of matter? In this case I have proved that one cannot form a supersymmetric black hole (such as extremal Reissner-Nordstrom) in finite time. Thus a third law holds for supersymmetric black holes. The proof involves ideas related to quasi-local energy. In this talk I shall review all of these developments.