Backreaction of quantum fields on black hole space-times

About the Project

In classical general relativity, Einstein’s equations involve the curvature of space-time on the left-hand-side, and the stress-energy tensor of matter on the right-hand-side. In a quantum theory of gravity, both sides of Einstein’s equations (that is, both the geometry and the matter) will be quantum in nature. However, a theory of quantum gravity remains elusive, and, in its absence, a less ambitious approach is semiclassical gravity, whereby the space-time geometry remains classical but the matter in the theory is quantized and described by a quantum field.

This project is concerned with the backreaction of quantum fields in a perturbative approach to semiclassical gravity. Starting with a fixed background space-time, the expectation value of the stress-energy tensor operator of a quantum field on this background is calculated. This expectation value is then used as a source term in Einstein’s equations, which are solved to give the effect that the quantum field has on the space-time geometry.

The aim of the project is to explore the backreaction of quantum fields on black hole space-times. First, the stress-energy tensor for a chosen quantum field is computed, employing recent analytic and numerical methodologies such as extended coordinates or pragmatic mode sum renormalization. Next, the linearized Einstein equations describing perturbations of the black hole space-time are derived analytically, and then solved numerically. The ultimate goal is the characterization of backreaction effects on key black hole properties, such as the light ring and black hole shadow, as well as exploring the consequences for black hole singularities.

For this project, a strong 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.