The Black-to-White Hole Transition
Abstract
Classically, an isolated black hole is a stable gravitational object. If however semiclassical effects are taken into account, an isolated black hole can be shown to slowly radiate its mass away in a process called evaporation. At the end of the evaporation process, when the size of the horizon becomes Planckian, the quantum nature of the gravitational field can no longer be neglected and the dynamics of the horizon is governed by quantum gravity. The main objective of this thesis is the systematic investigation of a tentative scenario for the “end of the life” of a black hole: the black-to-white hole transition.
Starting from the classical Oppenheimer-Snyder model, which is the simplest model of black hole formation by gravitational collapse, an effective metric that takes into account first-order quantum gravitational effects is derived using loop quantum gravity. In the resulting spacetime, the star undergoes a ``bounce'' at the end of its collapse and the interior trapped geometry of the black hole smoothly transitions into the anti-trapped geometry of the interior of a white hole. A natural assumption is then that, at the end of the evaporation process, the horizon of the black hole undergoes a quantum (tunneling) transition from trapping to anti-trapping consistently with the transition of geometry taking place in the interior of the hole. In this thesis, I construct and analyze a concrete effective metric describing the entire spacetime of this scenario, known as the black-to-white hole transition. This is a result of fundamental importance in improving our understanding of the physics of this phenomenon.
The quantum tunneling transition of the horizon in this scenario is a non-perturbative phenomenon that can only be studied using a background-independent theory of quantum gravity. I show that the covariant formulation of loop quantum gravity, also known as spin foam formalism, provides a clear framework to investigate this phenomenon and I compute the spin foam transition amplitude associated with it. A thorough investigation of this transition amplitude, which is currently out of reach due to the severe complexity of the latter, would allow us to give definitive answers to the remaining open questions about the black-to-white hole transition scenario.