# Wave Propagation Through Caustics: Applications in Gravitational Wave Physics

Lead Research Organisation:
University of Southampton

Department Name: School of Mathematics

### Abstract

Gravitational Waves -- propagating ripples in the fabric of space and time -- are a fundamental prediction of Einstein's theory of General Relativity. Nearly a century has passed since Einstein's masterwork, and yet gravitational waves remain frustratingly elusive! Astronomers have gathered strong evidence for their existence by measuring the rate of rotation of rapidly-spinning neutron stars ( pulsars ). Here on Earth, physicists are optimistic of direct detection within a decade.Gravitational waves (GWs) are important because they are generated by the most violent processes in the known Universe, such as supernovae, black hole mergers, and galaxy collisions. To the frustration of astronomers, such powerful processes are hidden behind shrouds of dust and strong fields. Light cannot penetrate this shroud, but gravitational waves can. By lifting the shroud, GWs will reveal the dynamic heart at the centre of such processes.Astronomy will enter a new era with the launch of the Laser Interferometer Space Antenna (LISA) in 2018 (est). A key aim of LISA is to detect gravitational waves emitted by binary black hole systems. In theory, the motion of a compact body orbiting a black hole can be reconstructed from the gravitational wave signal alone. A recent NASA-ESA report concludes that LISA will provide unambiguous and clean tests of the theory of general relativity in the strong field dynamical regime and be able to make detailed maps of spacetime near black holes. This is an exciting prospect, yet much theoretical work is needed if we are to separate out a small GW signal from a noisy background.In this project I will model so-called Extreme Mass Ratio Inspiral (EMRI) events, in which a small compact body spirals into a large black hole (e.g. Sag A*, residing at the centre of our galaxy). The gravitational wave signal emitted by EMRIs is a key target for LISA; hence this project is both timely and potentially significant.The most promising method for modelling EMRIs requires the calculation of a gravitational self-force which acts upon the small body. The self-force leads to a loss of orbital energy, causing the small body to spiral inwards, slowly at first, but with increasing rapidity. In curved spacetime -- for example, in the immediate vicinity of a black hole -- it turns out to be surprisingly difficult to compute the self-force, because it depends on the entire history of the small body's motion! In this project I will develop new mathematical methods to calculate the self-force, to complement the existing approach pioneered by members of the Southampton Relativity Group.The self-force arises from the interaction between a body and perturbations in its own gravitational field. Recent work suggests that, for EMRIs, the gravitational self-force may be primarily due to a non-local component which arises from perturbations that are lensed multiple times around the central black hole. To investigate this idea, I will make a mathematical study of the propagation of gravitational waves through focal points (also known as caustics). My primary motivation is to clarify the physical origin of the self-force, but other applications may also arise from this work.Since wave phenomena (diffraction, refraction, rainbows, glories, etc.) are ubiquitous across the physical sciences, I propose to make a multi-disciplinary study of the effects of caustics upon wave propagation. I will draw upon theoretical developments in seismology; catastrophe theory in optics; distribution theory in mathematics; and a range of other fields. I will also draw upon the breadth and depth of experience in the School of Mathematics at Southampton. Together with co-workers, I hope to make a significant contribution to the future development of precision Gravitational Wave Astronomy.

## People |
## ORCID iD |

Sam Richard Dolan (Principal Investigator) |

### Publications

Casals M
(2013)

*Quantization of fermions on Kerr space-time*in Physical Review D
Dolan S
(2013)

*Self-force via -mode regularization and evolution. III. Gravitational field on Schwarzschild spacetime*in Physical Review D
Dolan S
(2010)

*Quasinormal mode spectrum of a Kerr black hole in the eikonal limit*in Physical Review D
Dolan S
(2012)

*Resonances of a rotating black hole analogue*in Physical Review D
Dolan S
(2013)

*Superradiant instabilities of rotating black holes in the time domain*in Physical Review D
Dolan S
(2013)

*Scattering by a draining bathtub vortex*in Physical Review D
Dolan S
(2011)

*Self-force via -mode regularization and evolution. II. Scalar-field implementation on Kerr spacetime*in Physical Review D
Dolan S
(2011)

*Wave propagation and quasinormal mode excitation on Schwarzschild spacetime*in Physical Review D
Dolan S
(2011)

*Aharonov-Bohm effect in a draining bathtub vortex*in Physics Letters B
Dolan S
(2010)

*Quasinormal modes and Regge poles of the canonical acoustic hole*in Physical Review DDescription | * I developed a new method for computing the gravitational self-force that drives the inspiral and merger of a pair of compact bodies (such as black holes) under gravitational attraction. * I made the first GSF calculation for a rotating black hole * I showed the connection between caustics in wave propagation around black holes, and the spectrum of black hole resonances known as quasinormal modes. |

Exploitation Route | One hundred years after Einstein developed his theory of general relativity, we are now on the verge of directly detecting gravitational waves -- propagating ripples in spacetime -- here on Earth. My work is part of an ongoing effort to understand how gravitational waves are generated by black holes. My work is relevant to anyone interested in the consequences of Einstein's theory, and the wide community of scientists who are seeking to "hear" the Universe for the first time. |

Sectors | Other |

URL | https://inspirehep.net/search?ln=en&p=find+a+sam+dolan&of=hb&action_search=Search |

Description | My findings have been used by other researchers who are interested in black holes, their resonances (quasi-normal modes), and the propagation of waves on curved spacetimes. In particular, my work has advanced the "Gravitational Self-Force" programme, whose goal is to accurately model the motion and gravitational-wave emission of extreme mass ratio inspiral binary systems. Improved modelling of sources will contribute towards the experimental search for gravitational waves, and the nascent field of gravitational wave astronomy. |

First Year Of Impact | 2009 |

Sector | Other |

Impact Types | Societal |