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We investigate the interiors of 3+1 dimensional asymptotically flat chargedand rotating black holes as described by observers who fall into the blackholes at late times, long after any perturbations of the exterior region havedecayed. In the strict limit of late infall times, the initial experiences ofsuch observers are precisely described by the region of the limiting stationarygeometry to the past of its inner horizon. However, we argue that lateinfall-time observers encounter a null shockwave at the location of thewould-be outgoing inner horizon. In particular, for spherically symmetric blackhole spacetimes we demonstrate that freely-falling observers experience ametric discontinuity across this shock, that is, a gravitational shock-wave.Furthermore, the magnitude of this shock is at least of order unity. A similarphenomenon of metric discontinuity appears to take place at the inner horizonof a generically-perturbed spinning black hole. We compare the properties ofthis null shockwave singularity with those of the null weak singularity thatforms at the Cauchy horizon.

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