PhD students
Prospective PhD students
All applications for PhD study at the University of Sheffield must be made online. Please do not send applications directly to me. The School of Mathematics and Statistics' prospective postgraduates webpage has information about PhD opportunities within the School, applications and funding. The University's Doctoral Academy website has a great deal of useful information.
To work under my supervision, I usually expect PhD students to have (or expect to obtain) the equivalent of a UK first class undergraduate degree at either BSc or MMath/MPhys level. If you have a BSc undergraduate degree, then usually a Master's level qualification in either Theoretical Physics or Mathematics is also required. A strong background in general relativity and quantum theory is necessary; knowledge of quantum field theory in flat space-time is an advantage. Experience with algebraic and numerical computing (whether using Mathematica, Maple, Matlab or a programming language) is also an advantage.
Possible PhD projects
Quantum field theory on anti-de Sitter black holes - The renormalized vacuum polarization (VP) of a quantum scalar field and renormalized expectation value of the stress-energy tensor (RSET) are notoriously challenging quantities to compute, despite the central roles they play in quantum field theory in curved space-time. There is a well-established methodology for computing both the VP and RSET for a quantum scalar field on a static, spherically symmetric, four-dimensional black hole space-time. This project would extend this methodology to asymptotically anti-de Sitter black holes.
Doubly-rotating black holes - Defining quantum states on rotating black holes is challenging due to superradiance. The reduced symmetry also makes computing expectation values technically challenging. If we work in five-dimensional space-time, then doubly-rotating black holes have an enhanced symmetry which may aid the practical computation of expectation values.
Effect of charge superradiance on a quantum field - Superradiant modes of a scalar field on Kerr space-time are one of the many complications in defining quantum states on a rotating black hole. Charge superradiance occurs for a charged scalar field on a charged black hole. This project would investigate how quantum states can be defined in this case, paying particular attention to the role of superradiant modes.
Quantum fermion field on a three-dimensional BTZ black hole - Quantum field theory on three-dimensional black holes is simpler than in four (or more) dimensions. A quantum scalar field has been extensively studied on a three-dimensional BTZ black hole, but a quantum fermion field rather less so. It would be interesting to compute the RSET for a quantum fermion field on both nonrotating and rotating BTZ black holes. A key aspect will be studying appropriate boundary conditions for a fermion field on the space-time boundary.
Hawking radiation from quantum gravity black holes - Quantum effects are very important for black holes, but in the absence of a full theory of quantum gravity, effective models of black holes incorporating quantum effects are useful. In a paper with Piero Nicolini, we studied the Hawking radiation of a quantum scalar field from a black hole described by a classical effective metric which models quantum gravity effects. The radiation has a number of features rather different from the emission from a usual Schwarzschild black hole. It would be interesting to extend this work to other quantum fields and more general effective black hole metrics.
Current PhD students
Jacob Thompson (started October 2022)
Alessandro Monteverdi (started October 2021)
Siva Namasivayam (started January 2021)
George Montagnon (part-time, started October 2020)