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 spacetime 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
 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.
 Quantum field theory on antide Sitter black holes  The renormalized vacuum polarization (VP) of a quantum scalar field and renormalized expectation value of the stressenergy tensor (RSET) are notoriously challenging quantities to compute, despite the central roles they play in quantum field theory in curved spacetime. There is a wellestablished methodology for computing both the VP and RSET for a quantum scalar field on a static, spherically symmetric, fourdimensional black hole spacetime. The general idea is to write these expectation values as sums of various manifestly finite quantities which can be computed numerically. The conventional approach does not work well in general for asymptotically antide Sitter black holes, as the standard quantities diverge on the spacetime boundary. The aim of this project would be to write the expectation values in terms of new quantities which remain finite on the spacetime boundary, and hence to compute the VP and RSET on asymptotically antide Sitter black holes.
 Effect of charge superradiance on a quantum field  Superradiant modes of a scalar field on Kerr spacetime 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 threedimensional BTZ black hole  Quantum field theory on threedimensional black holes is simpler than in four (or more) dimensions. A quantum scalar field has been extensively studied on a threedimensional 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 spacetime boundary.
Current PhD students
 Thomas Morley (started October 2016)
 David Dempsey (started October 2013), jointly supervised with Sam Dolan
Past PhD students
