Dynamical evolution and stability of quantum corrected Schwarzschild black holes in semiclassical gravity

The Schwarzschild solution describes a classical static black hole in general relativity. When general relativity is extended by including semiclassical corrections in the form of a renormalized energy-momentum tensor, the horizon of the Schwarzschild black hole disappears and is replaced by a wormhole. We study the stability of this quantum corrected static Schwarzschild solution in semiclassical gravity by using it as the initial data of a dynamical evolution. We find that the quantum corrected solution is unstable and that the wormhole can expand or collapse when perturbed. In vacuum, the wormhole expands, but in the presence of even a small amount of classical matter, the wormhole collapses, forming a horizon and evolving to an evaporating black hole.