Spin and superradiance in General Relativity

About the Project

In General Relativity, bodies in freefall follow geodesics in spacetime. For example, the Earth follows a geodesic in the spacetime of the Sun, to a good approximation. However, this is not strictly true for compact bodies with angular momentum. Rapidly spinning bodies, such as neutron stars and black holes, are pushed away from geodesic motion by a spin-curvature force, modelled with the Mathisson-Papapetrou-Dixon equations. Moreover, a massive spinning body pulls spacetime itself around with it. This generates Lense-Thirring precession, a gravitomagnetic frame-dragging effect that was confirmed by Gravity Probe B in 2011. In the extreme environment of black holes, frame-dragging near an event horizon creates superradiance: an amplification mechanism harnessing the rotational energy of a black hole.

The aim of this project is to model and characterise the effects of spin on the dynamics of neutron stars and black holes in General Relativity. As a first example, geodesic motion on Kerr spacetime has long been known to be integrable (in the sense of Liouville), but very recent work on the MPD equations has shown that the motion of spinning bodies is also integrable to first order in the spin. Work is underway to determine whether motion is integrable also at second order (or even all orders) and, if not, to characterise the chaotic motion of spinning bodies on this spacetime. As a second example, frame-dragging in spacetime leads to a polarisation-dependent effect at sub-leading order in geometric-optics expansion for electromagnetic waves; this can be modelled with the spin-optics framework. As a third example, superradiance can lead to an exponentially-growing instability in ultralight bosonic fields if the Compton wavelength is comparable with the event horizon radius -- this motivates the search for evidence of ultra-light particles (e.g. axions) and beyond Standard Model physics in astronomical data.

The student will undertake one or more projects in the areas above. In conjunction, the student will join a team of scientists in the LISA Consortium to calculate and characterise the effect of the spin on the gravitational waves generated by Extreme Mass-Ratio Inspirals, in advance of the launch of the Laser Interferometer Space Antenna (a gravitational wave detector) in 2035.

The project would suit a student with strong analytical skills, who can push forward a technically-demanding project(s) that feed into a larger scientific endeavour. Good mathematical and communication skills are essential. In addition, the applicant should have good coding skills in Python or Mathematica, and/or the desire to improve them. 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.