# PhD projects

We welcome applications to study for a PhD in our group. For details about the areas of research, look at our staff members' websites. If you have further questions, please contact the staff member you are interested in working with.

Typically a small number of fully funded places in the School are available each year and decisions on these are made between January and April for an October start. Other start dates during the year are possible, but PhD funding is only allocated once a year.

## PhD application advice

We recommend reading our PhD application advice as it explains the process of how we select candidates for PhD places and funding, which may be different from how it works in other universities and countries.

Do not send applications or CVs directly to us by email, use the online application form.

There are internal deadlines for consideration for PhD studentships (in particular EPSRC). Your application should be complete before any deadline. In particular, please include either your Master's dissertation (or equivalent) or an example of written project work.

We usually await the first deadline for PhD studentships (often at the end of January) before selecting some applicants for an online interview. We might ask applicants to prepare a short presentation as part of the interview. After a successful interview applicants will be put forward for funding, which is then decided at the level of the School of Mathematics and Statistics in a complicated process.

Below are some examples of projects we could supervise in 2024, organised by general research area. In general, finding a suitable project can be part of the discussions around a PhD interview. Given how our PhD funding works, in a particular year we may or may not find funding for any of these projects.

## Projects in Black Holes and Gravitational Waves

## Black hole perturbation theory for gravitational-wave source modelling (Sam Dolan)

Orbiting black holes generate distinctive 'chirp' signals, which have been successfully detected at gravitational-wave observatories such as LIGO since 2015. A key aim of the forthcoming LISA mission (a space-based interferometer) is to detect signals from supermassive black holes, such as the one at the centre of our galaxy.

In this project, we will aim to model the final ~100,000 orbital cycles of a stellar-mass black hole orbiting a supermassive black hole, by applying gravitational self-force theory. In particular, we will extend recent work by Dolan, Kavanagh and Wardell (arXiv:2108.06344) to construct Lorenz-gauge metric perturbations of the Kerr black hole directly from mode sums, for the first time.

## Projects in Cosmology

## Constraints on models beyond the standard LCDM by using current and future cosmological data (Eleonora Di Valentino)

The cosmic microwave background (CMB) temperature and polarisation anisotropy measurements from the Planck mission have provided a strong confirmation of the LCDM model of structure formation, based on the cosmological constant lambda and the presence of cold dark matter, ie on completely unknown quantities. Moreover, there are a few interesting tensions that, albeit with different statistical significance, leave the door open to possible extensions to LCDM.

In this project we are going to consider extended scenarios beyond the standard LCDM, by constraining different dark energy models, in order to explain and relieve tensions in the current cosmological data. For example, between the Planck data and the direct measurements of the Hubble constant by the SH0ES collaboration and the parameters from weak lensing surveys, such as DES and KiDS-1000.

Moreover, we will be exploring the neutrino sector, the effective number of neutrino species and the total neutrino mass. Since we are close to testing the neutrino mass hierarchy with existing cosmological probes, we will be considering a combination of datasets and scenarios.

Finally, we will study how much these constraints could be improved by considering future data from CMB experiments, for example CMB-S4, DESI, PIXIE, PRISM, PICO.

The project requires basic knowledge of cosmology, and we will be using publicly available codes like CAMB/CLASS or the Monte Carlo Markov Chain package Cobaya.

## Projects in Quantum Field Theory in Curved Spacetime

## Quantum fields on black-hole spacetimes (Elizabeth Winstanley)

Classically a black hole can only absorb and not emit particles. Black holes do however emit quantum Hawking radiation. This project is concerned with the behaviour of quantum fields on black hole spacetimes.

The construction and properties of quantum states on black hole backgrounds will be studied, including the computation of renormalized expectation values of observables such as the vacuum polarisation or stress-energy tensor. A particular focus will be on black holes with either rotation or charge, where superradiance effects play an important role.

## Projects in Quantum Gravity and Quantum Cosmology

## Time and relational dynamics in models of quantum gravity (Steffen Gielen)

One of the main obstacles in unifying general relativity and quantum mechanics is known as the 'problem of time': in general relativity, unlike in usual quantum mechanics, statements about evolution in a particular time coordinate have no invariant physical meaning. Physically meaningful statements need to be made in relational terms, as the change in a 'system' relative to the change in the 'clock'. In cosmology, the clock can for instance be a scalar field, or the volume of the universe.

In this project you will study relational formulations of dynamics in classical relativity and their realisations in quantum models of cosmology or quantum black holes. Depending on interest, some specific questions can include the role of unitarity in quantum gravity (related to evolution and hence the definition of time), approaches using a standard of time based on dark energy (known as unimodular gravity), or the clocks used by observers encountering singularities in black holes and cosmology. You could also work on the explicit construction of new models for material clocks in approaches to quantum gravity such as group field theory. Such constructions can be used to compare quantisations based on different clocks, and potentially link these ambiguities to observational effects.