Georgia Institute of Technology College of Sciences

The Reissner–Nordström spacetime models a spherically symmetric and time-independent charged black hole in general relativity. The Cauchy horizon in the interior of such a black hole is subject to an infinite blueshift instability. In 1989, Poisson and Israel discovered a nonlinear manifestation of this instability in the spherically symmetric setting called "mass inflation," where the Hawking mass becomes identically infinite at the Cauchy horizon. 

We complete the first proof of mass inflation for a wave-type matter model, namely the spherically symmetric Einstein–Maxwell–scalar field system. This result follows from a large-data decay result for the scalar field in the black hole exterior combined with works of Dafermos, Luk–Oh, and Luk–Oh–Shlapentokh-Rothman.