Violation of the third law of black hole mechanics in vacuum gravity

We demonstrate numerically the existence of solutions of five-dimensional vacuum gravity describ- ing the formation, in finite time, of an extremal rotating black hole from a pre-existing Schwarzschild black hole. This is the first example of a violation of the third law of black hole mechanics in vac- uum gravity and demonstrates that the third law is false independently of any matter model. We also demonstrate the existence of solutions describing the formation, in finite time, of an extremal rotating black hole from vacuum initial data that does not contain a black hole.