On the role of shell-crossing singularities in quantum black hole evolution

Abstract

The gravitational collapse of a spherically symmetric star within classical general relativity typically results in the formation of a black hole and the development of a central spacetime singularity—the Schwarzschild singularity. However, this classical scenario is expected to be significantly modified when quantum gravitational effects are taken into account. In this thesis, I investigate the effective dynamics of gravitational collapse incorporating quantum corrections inspired by loop quantum gravity. The analysis reveals a modified picture in which the stellar core undergoes a quantum bounce at Planckian energy densities, followed by the emergence of shell-crossing singularities shortly after the bounce. A comprehensive study of these phenomena is presented, both in the case of pressureless matter (dust) and in the presence of non-zero pressure, across a wide class of initial data. Particular attention is devoted to the central role played by shell-crossing singularities in the quantum-corrected dynamics. Their general properties are analyzed in detail, and possible strategies to extend the spacetime beyond these singularities are proposed. Finally, as a first step towards extending these results to the case of axisymmetric gravitational collapse, I analyze a metric for a rotating black hole inspired by loop quantum gravity.