Electronic Thesis and Dissertation Repository

Thesis Format

Integrated Article


Doctor of Philosophy




Vidotto, Francesca

2nd Supervisor

Christensen, Dan


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.

Summary for Lay Audience

There is evidence in the sky of the presence of a huge number of black holes. We even took a few good pictures of them. However, it is surprising how much we still do not know or understand about them. Intuitively, a black hole is a region of spacetime where space is falling faster than the speed of light, and anything that tries to move outwards is nonetheless carried inwards by the faster-than-light inflow of space. This means that nothing can escape a black hole, not even light. This is bizarre. But it is not even its oddest feature. Black holes are formed when massive enough stars at the end of their life, that is when the nuclear reactions in their interior stop, collapse under their own gravitational force. After a black hole is formed, the star keeps collapsing until all of its mass is concentrated in a single point of infinite density. “Infinity” is a mathematical concept that has no counterpart in the physical world and it should not be predicted for any physical quantity. This point is then called a ``singular'' point of spacetime and it is taken to signal the breakdown of the classical theory of gravity.

However, the big revolution of modern physics of the twentieth century taught us that the microscopic world does not follow the (deterministic) rules of classical physics, but it actually follows the (probabilistic) rules of a new theory called quantum physics. The theory describing the quantum rules of the gravitational field is called quantum gravity, and we still do not have a complete understanding of it. Using a specific tentative theory of quantum gravity known as loop quantum gravity, I re-investigate the collapse of a star and the subsequent formation of a black hole in a quantum context. What I find is that the collapse of the star does not end in a singular point of infinite density anymore, but it reaches instead a point of maximum, but finite, density after which the star ``bounces'' and starts to expand. Furthermore, consistently with the bounce of the star, the black hole transitions into a white hole. The latter is the ``opposite'' of a black hole: a white hole is a region of spacetime where space is expanding faster than the speed of light, and so everything in its interior is bound to come out of it. I then compute the quantum probability for this process to take place.

Creative Commons License

Creative Commons Attribution-Noncommercial 4.0 License
This work is licensed under a Creative Commons Attribution-Noncommercial-Share Alike 4.0 License.