Outgoing gravitational shock wave at the inner horizon: The late-time limit of black hole interiors

We investigate the interiors of (3+1)-dimensional, asymptotically flat charged and rotating black holes as described by observers who fall into the black holes at late time, long after any perturbations of the exterior region have decayed. In the strict limit of late infall time, the initial experiences of such observers are precisely described by the region of the limiting stationary geometry to the past of its inner horizon. However, we argue that late-infall-time observers encounter a null shock wave at the location of the would-be outgoing inner horizon. In particular, for spherically symmetric black hole spacetimes, we demonstrate that freely falling observers experience a metric discontinuity across this shock; that is, a gravitational shock wave. Furthermore, the magnitude of this shock is at least of order unity. A similar phenomenon of metric discontinuity appears to take place at the inner horizon of a generically perturbed spinning black hole. We compare the properties of this null shock-wave singularity with those of the null weak singularity that forms at the Cauchy horizon. © 2012 American Physical Society