Research projects for PhD students: Ideas (2016)
1. Black hole instabilities and hairy black holes
In a Penrose process, a black hole may liberate energy and angular momentum (and/or charge) whilst still increasing its horizon area. It would appear that Penrose processes are encouraged by the second law of black hole mechanics and thus the second law of thermodynamics.
An intriguing example of a Penrose process is superradiance, in which a low-frequency wave packet in a bosonic field is amplified by a black hole. If the field is confined in the vicinity of hole (by a mirror, or more naturally, by its mass) an explosive process known as a black hole bomb may arise. This raises the possibility that a black hole in vacuum will evolve towards a more stable 'hairy' configuration.
Recently, a new class of rotating black holes with scalar-field hair were been identified by Herdeiro and Radu. These solutions are smoothly connected to 'solitonic' solutions: the boson stars. It is conjectured that the new solutions are the endpoint of the black hole bomb instability.
In this project, the student will seek to shed new light on Wheeler's conjecture that 'black holes have no hair'. It would suit a student that wishes to make a timely contribution in a rapidly-developing area.
2. Scattering and absorption of fields by black holes
Interest in the scattering and absorption of various fundamental fields (scalar, Dirac, EM, Proca, gravitational) by black holes can be traced back to (at least) 1968 and the work of Matzner. There is growing interest in the possibility of observing the 'shadow' of the black hole at the centre of the galaxy. Intriguingly, the shadow cast by a pair of black holes (a binary) has fractal properties.
In this project the student would calculate scattering and absorption cross sections, and relate their key features (eg shadows, glories or interference patterns) to the properties of the black hole geodesics (photon orbits, ergosphere, parallel transport of spin, etc). The student could also consider scattering by analogue black holes, which is potentially observable in the laboratory.
3. Self-force calculations for black hole inspirals
Since 1997, the gravitational self-force programme (built around black hole perturbation theory and Dirac's conception of radiation reaction) has developed to model the inspiral of extreme mass-ratio inspirals. Gravitational waves from extreme mass-ratio binaries are in the observable band of the proposed eLISA gravitational wave detector.
Recently, it has been shown by Damour, Barack and others, that the gravitational self-force approach can also inform the effective one-body model, which is presently used in the data analysis pipeline in 2016 at ground-based detectors seeking comparable-mass binaries.
In this project, the student would seek to calculate the electromagnetic or gravitational self-force for a spinning binary system: a challenge with many conceptual, technical and numerical hurdles.
4. Exact solutions in general relativity (GR)
Exact solutions in GR are cherished, due to their rarity. Typically, exact solutions are only available in spacetimes with symmetries (Killing vectors, spinors and/or tensors); as one removes symmetry assumptions, the challenge of finding exact solutions becomes more formidable.
In this project, the student would study exact solutions which may be relevant to the gravitational two-body problem. First, the student would review what is known about static two-body solutions, such as Weyl-Bach family and the Majumdar-Papapetrou family, and their extensions. Then, the student will seek a "helical" two-body solution which admits a single helical Killing vector. (Note that the boundary conditions required for this symmetry may render the solutions not asymptotically flat.)
This project would suit an ambitious student with a high level of analytical and technical skill.