Black hole perturbation theory for gravitational-wave astronomy

About the Project

Pairs of black holes generate distinctive 'chirp' signals as they coalesce. These signals have been successfully detected at gravitational-wave observatories since 2015. Using these signals, we can test the theory of relativity in the strong-field regime and we can learn more about the "zoo" of black holes that populate our universe. The next decade will see the launch of the first detector in space: the Laser Interferometer Space Antenna (LISA) satellite. LISA will detect lower-frequency gravitational waves from supermassive black holes that lie at the heart of most galaxies. A key target for LISA are the so-called Extreme Mass-Ratio Inspirals (EMRIs): stellar-mass black holes in orbit around supermassive black holes. Their signals are weak but quasi-periodic, and the scientific challenge in the 2030s will be, first, to find these "needles in the haystack" in a noisy data stream; next, to accurately estimate their parameters (mass, spin, orbital inclination etc); and finally to use these to test General Relativity and its competitor theories. In short, with EMRI signals, we aim to "map" the spacetime around a supermassive black hole and put Einstein's theory to its most stringent test yet.

The aim of this project is to accurately model the final 100,000 orbital cycles of an EMRI using the gravitational self-force method. We will build on recent work by Dolan, Kavanagh and Wardell ([1], [2], [3]) to compute the metric perturbation at first order in Lorenz gauge that is generated by a compact body on a generic orbit around a larger, spinning (Kerr) black hole. This metric perturbation is the key input for second-order-in-mass-ratio calculations that are presently at the forefront of the field. To facilitate such second-order calculations in time for the launch of the LISA mission in 2035, the PhD student will build collaborations with other scientists working on this problem in the community.

The project would suit a student with a blend of analytical and coding skills, who can push forward a technically-demanding sub-project that feeds into a larger scientific endeavour. Good mathematical and communication skills are essential; and it is expected that the applicant will have taken a course in General Relativity.

Funding Notes

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

References

[1] Metric perturbations of Kerr spacetime in Lorenz gauge: circular equatorial orbits.
S. R. Dolan, L. Durkan, C. Kavanagh and B. Wardell, Class. Quant. Grav. 41 (2024) 15, 155011.
[2] Gravitational Perturbations of Rotating Black Holes in Lorenz Gauge.
S. R. Dolan, C. Kavanagh and B. Wardell, Phys. Rev. Lett. 128 (2022) 15, 151101.
[3] Sourced metric perturbations of Kerr spacetime in Lorenz gauge.
B. Wardell, C. Kavanagh and S. R. Dolan, Class. Quant. Grav. 42 (2025) 20, 205007.