Nonlinear instability of Kerr-type Cauchy horizons

Abstract

Using the general solution to the Einstein equations on intersecting null surfaces developed by Hayward we investigate the nonlinear instability of the Cauchy horizon inside a realistic black hole. Making a minimal assumption about the free gravitational data allows us to solve the field equations along a null surface crossing the Cauchy horizon. As in the spherical case, the results indicate that a diverging influx of gravitational energy, in concert with an outflux across the Cauchy horizon, is responsible for the singularity. The spacetime is asymptotically Petrov type N, the same algebraic type as a gravitational shock wave. Implications for the continuation of spacetime through the singularity are briefly discussed.