Kate Clements | Applied Math, University of Waterloo
Black Hole to White Hole Quantum Tunnelling
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. We interpret this transition as conventional quantum tunnelling. In order to evaluate the tunnelling probability, 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 normal vectors 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 the matter that falls into a black hole.