Charged quantum fermion fields on charged black hole space-times

About the Project

This project is concerned with quantum field theory in curved space-time, a semiclassical approach to the as-yet-elusive theory of quantum gravity. In this set-up, the space-time geometry is fixed and classical, while the matter is quantized (and described by a quantum field). In this project the background space-time is a charged Reissner-Nordstrom black hole, and the quantum field is a charged fermion field.

There are three key aspects to the project. The first is studying the canonical quantization of the charged fermion field on the charged black hole background, with the aim of constructing a thermal, Hartle-Hawking state. This part of the project will build upon recent work [1] demonstrating that charged fermions exhibit quantum superradiance and in which vacuum states were constructed. The results will be compared with those for a charged scalar field [2].

The second part of the project involves computing the renormalized expectation value of the stress-energy tensor for the charged fermion field, using Hadamard renormalization. The renormalization counterterms will be derived using a generalization of the approach in [3] for a charged scalar field (but adapted to fermions), and then applied to numerical computations using either extended coordinates [4] or pragmatic mode sum [5] methodology.

Finally, the project will explore the backreaction of the charged fermion field on the charged black hole by solving the linearized Einstein equations describing perturbations of the original black hole space-time. The source term in these linearized Einstein equations is the stress-energy tensor computed above.

For this project, an excellent background in both general relativity and quantum field theory is required. Familiarity with quantum field theory in curved space-time is an advantage, but not essential. This project will involve a mix of analytic and numerical work; therefore strong technical skills in both pen-and-paper calculations and coding using either Python or Mathematica are essential. Experience with a computer algebra system such as Mathematica is an advantage. We are also looking for good written and verbal communication skills.

The Gravitation and Cosmology Group at Sheffield consists of 6 members of academic staff, together with 12 PhD students and several postdoctoral researchers. We are a friendly and welcoming group, with an active programme of seminars and a journal club.

Funding Notes

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