Abstract

A few years ago, Kehle and Unger proved that, by sending finely tuned pulses of a charged scalar field into a black hole, it is possible to form an extremal Reissner-Nordström black hole in finite time, i.e. the third law is false. The proof makes use of characteristic gluing: a framework to build solutions to Einstein’s equations by gluing two regions of spacetime along a null cone. In this talk, I will present numerical implementations of characteristic gluing. Firstly, I will revisit the model of Kehle and Unger and numerically construct solutions to the characteristic gluing problem. I will show how these solutions depend on the parameters of the theory (charge and mass of the scalar field, cosmological constant), and discuss the differences between solutions of different levels of regularity. In the second part of the talk, I will apply characteristic gluing to the vacuum Einstein equations in 5d, and will present a solution that forms an extremal Myers-Perry black hole in finite time. This is the first counterexample of the third law in vacuum gravity and shows that the law is false independently of any matter model. This talk is based on work done with John Crump, Harvey Reall and Jorge Santos.