Unitary quantum gravity and the fate of black holes

About the Project

Black holes have now been observed in detail via astrophysical observations, detections of gravitational waves and pictures of the event horizon. However, their theoretical description within general relativity is incomplete, since it contains a singularity where the laws of physics break down. Quantum theories of gravity may offer a very different perspective on the fundamental description of black holes.

A fundamental principle of quantum mechanics is the unitarity of time evolution, which implies that a quantum state cannot “disappear” but exists at all times. Using the principle of unitarity in quantum models of black holes, it has recently been shown that the singularity inside a black hole is replaced by a transition from a black hole to a white hole.

In this project you will extend these ideas to other models of black holes, for example to charged black holes. The inclusion of matter could lead to a better understanding of gravitational collapse when quantum gravity effects are included. Whether a more complicated black-hole model again undergoes transition to a white hole can depend on specific properties of the models. Another direction could be to study Hawking radiation, which could explain what happens to the black hole-white hole transition when a black hole radiates away. In principle, insights gained from these calculations can be related to possible observational signatures.

The project will mostly be based on analytical calculations but it is expected that some numerical work will be needed as well; hence, at least an interest in programming would be desirable. Good prior knowledge of general relativity and quantum field theory at MSc level is essential; some knowledge of black holes in general relativity would be desirable. The standard entry requirement for a PhD in mathematics at Sheffield is a first class BSc and a UK first-class or upper second class (2:1) MMath or MSc Merit (or international equivalent), in Mathematics or a related subject.

The Gravitation & Cosmology group at Sheffield consists of 6 academics, currently 12 PhD students and several postdoctoral researchers. We offer a friendly and active research environment with several weekly seminar and journal club events.

Funding Notes

This project is for Self-funded students or students with external funding.