Breakdown of Semiclassical Gravity in Four-Dimensional Black Hole Evaporation

We study black hole formation and evaporation in a four-dimensional semiclassical model that preserves diffeomorphism invariance and reproduces the one-loop trace anomaly. Solving the quantum-corrected Einstein equations for the collapse of a spherically symmetric null shell, we follow the formation and evaporation of a black hole with back-reaction included. The semiclassical solutions develop a spacelike thunderbolt singularity that emerges after the apparent horizon has receded and extends far from the black hole where the semiclassical curvature is a priori expected to be parametrically small. This behavior arises from a nonlinear instability of the higher-derivative semiclassical equations and is generic in models with anomaly-induced quantum corrections. The thunderbolt signals a breakdown of semiclassical effective field theory over macroscopic distances and undermines the standard formulation of the black hole information paradox.