Effective Black Holes in Quantum Gravity

Abstract

This dissertation explores quantum gravity applications to resolve black hole singularities, investigates the potential transition from black holes to white holes, and characterize the resulting spacetime in each scenario. The following work utilizes various approaches, including canonical loop quantum gravity (LQG) and the generalized uncertainty principle (GUP), while also adopting a more flexible framework that is not tied to any single quantum gravity theory. Instead, this research relies on guiding principles expected to emerge from a complete theory of quantum gravity. Through this exploration, the dissertation aims to contribute to the resolution of key issues in black hole physics within a quantum gravity setting.

The first significant contribution of this thesis involves the application of the Raychaudhuri equation to assess the existence of singularities. In particular, loop quantum gravity corrections to the Raychaudhuri equation are derived for the interior of a Schwarzschild black hole and near the classical singularity. The analysis demonstrates that the resulting effective equation leads to the defocusing of geodesics, caused by the emergence of repulsive terms. This effect prevents the formation of conjugate points, renders the singularity theorems inapplicable, and ultimately facilitates the resolution of the singularity in this spacetime.

Building on this, the next part of the work extends similar ideas within the framework of the generalized uncertainty principle. To address challenges identified in a previous model of the interior of a generalized uncertainty-inspired black hole, an "improved scheme'' is introduced, drawing inspiration from loop quantum gravity. In this scheme, quantum parameters become momentum-dependent, allowing the interior to be reworked and extended to the full spacetime. The resulting metric is found to be asymptotically flat, and its associated Kretschmann scalar remains regular throughout. Furthermore, it is shown that both the null expansion and Raychaudhuri equation are regular across the entire spacetime, indicating the resolution of the classical singularity.

The final chapters do not focus on a specific theory of quantum gravity but instead construct a class of time-dependent, asymptotically flat, spherically symmetric metrics to model gravitational collapse in quantum gravity. By imposing a quantum bounce, these metrics prevent singularity formation. They exhibit general properties expected from any quantum gravity theory, without committing to a particular approach. These metrics capture key insights into the dynamics of singularity resolution, as well as horizon formation and evaporation, following either a matter bounce or a black hole to white hole transition.