My work mainly concerns the application of tools from the mathematical analysis of partial differential equations (PDEs) to solve problems in theoretical physics, primarily connected to general relativity. You can find an up-to-date chronological list of all my publications with full bibliographic information here. For a lay summary of a few of my research papers grouped loosely by topic, see below.

Effective Field Theories

Often in a physical problem there are some degrees of freedom that we treat as unobservable because the energy required to excite them is much greater than the energy scale of the problem. For example, when modelling a pendulum with a rigid arm we ignore the vibrational modes of the arm. Or in quantum physics it may be that the energy scales available to us, for example in a collider, are not sufficient to create a particular heavy particle. These unobservable degrees of freedom can still affect the physics that we do observe. A tool that is often used to study this is the machinery of effective field theory (EFT). In a preprint with Harvey Reall I have explored some classical EFTs and given an account of how to handle the troublesome PDEs that can arise.

Anti-de Sitter Spacetimes

Anti-de sitter spacetimes are solutions of Einstein's equations with a negative cosmological constant. They are interesting mathematically as the structure of infinity for these spacetimes means that physical fields typically require that boundary conditions are imposed on a singular boundary. They are also of great interest to physicists in the context of the conjectured AdS/CFT correspondence. With collaborators, I have written several papers about the analysis of these spacetimes.

Quasinormal modes

A perturbed black hole will radiate energy at a fixed set of (complex) frequencies, which are independent of the manner in which it has been perturbed. This is similar to the way that a struck guitar string will produce sound at frequencies that are multiples of the fundamental frequency. In the case of a black hole, the characteristic oscillations giving rise to this radiation are called quasinormal modes, and the corresponding frequencies quasinormal frequencies. The quasinormal spectrum of a black hole carries information about its geometry. I have been interested, with Dejan Gajic, in how one can approach the somewhat delicate problem of finding quasinormal modes.

The geometry of sound and light propagation

Together with Gary Gibbons and other collaborators I have investigated the connections between aspects of geometry and the propagation of sound and light rays. One particularly interesting connection that we explored is the relation between sound propagating in a wind and a magnetic particle moving in a curved space. This is explained in a review article aimed at undergraduates:

Some more articles on this topic that I've been involved in include

Hidden symmetries

Symmetries play a fundamental role in modern physics due to their connection with conserved quantities through Noether's theorem. Usually the nature of the symmetry is readily apparent - for example the rotational invariance of a (non-rotating) star. Sometimes, however, symmetries occur that are not easily seen in the physical space set-up of the problem. A classical example is the symmetry which permits us to solve the Kepler problem of a planet orbiting a star exactly. Such symmetries are known as hidden symmetries.