Black Hole to White Hole Quantum Tunnelling

Abstract

In this thesis, we explore the proposal that near the end of its lifetime, a Schwarzschild black hole will undergo a quantum transition into a 'white hole': an object which is precisely the time-reversal of the black hole. This transition takes the form of quantum tunnelling. In order to evaluate the tunnelling amplitude, we characterize the region where quantum gravity effects dominate as enclosed by intersecting hypersurfaces on which the trace of the extrinsic curvature is equal to zero. This allows us to recover the tunnelling amplitude as specified by the boost angle between the normals to these hypersurfaces. The long-term aim of this work is to find the complex solutions to the vacuum Einstein equations in the quantum gravity region, and thus provide a complete explanation for what happens to a black hole after it evaporates.