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Details of Grant 

EPSRC Reference: EP/M025802/1
Title: New invariants for the gravitational two-body problem
Principal Investigator: Dolan, Dr SR
Other Investigators:
Researcher Co-Investigators:
Project Partners:
Department: Mathematics and Statistics
Organisation: University of Sheffield
Scheme: First Grant - Revised 2009
Starts: 30 July 2015 Ends: 29 July 2017 Value (£): 90,245
EPSRC Research Topic Classifications:
Mathematical Physics
EPSRC Industrial Sector Classifications:
No relevance to Underpinning Sectors
Related Grants:
Panel History:
Panel DatePanel NameOutcome
03 Mar 2015 EPSRC Mathematics Prioritisation Panel March 2015 Announced
Summary on Grant Application Form
Our perception of the Universe, at present, is based on "sight". Ever since Galileo spied the moons of Jupiter in 1610, we have been driven to improve the sensitivity and resolution of telescopes. These are our eyes on the Universe, working across the electromagnetic spectrum. Yet, with only "eyes", our perception is limited; much of the Universe remains dark, or shrouded from view behind clouds of dust and gas.

What if we could "hear" the Universe? This is not as fanciful as it may seem. Einstein's theory of General Relativity predicts the existence of "gravitational waves": ripples in the fabric of spacetime which propagate at the speed of light. Einstein's theory, now a century old, has passed every experimental test so far devised. Indeed, the existence of gravitational waves was confirmed by careful decade-long observations of a pulsar's orbit (brilliant work which won the Nobel prize in 1993).

It is widely anticipated that we stand on the cusp of developing "hearing". Enhanced detectors such as LIGO and VIRGO, coming online in the next few years, should enable us to "hear" gravitational waves for the first time. Gravitational waves are generated by the most powerful processes in the Universe, such as the orbits of supermassive black holes. Unlike our "eyes", our "ears" will be only weakly directional, and thus will hear a wide variety of sources and ambient noise. The key challenge will be to separate the interesting sources from the background. The challenge is akin to trying to listen to a friend over the hubbub at a noisy party: ears are not sufficient, a highly-evolved brain is essential too! To succeed, it is crucial to know precisely what we are listening for. Specifically, we need highly accurate models of gravitational wave signals emanating from compact binaries.

In this project, I aim to improve and upgrade our modelling of such signals. To achieve this aim, I must address a foundational problem in relativity: predicting the motion of two compact bodies, such as black holes, moving under mutual gravitational attraction. Why hasn't such a simple problem been "solved" already? Because it's not so simple! Einstein's theory describes, simultaneously, how the stage affects the actors and how the actors affect the stage. In the words of John Wheeler, "Matter tells space how to curve. Space tells matter how to move". In other words, finding "exact" mathematical solutions in dynamical scenarios is hard or impossible! Instead, we must develop and apply a range of numerical and approximation tools.

My key claim is that there are certain "invariants", related to physically-observable quantities (such as redshift, precession angle; tidal stress, etc.), that are yet to be computed for the gravitational two-body problem over its 100-year history. Invariants are crucial, as they allow us to compare, calibrate and enhance the various mathematical methods currently in use. Fancifully, I imagine these invariants to be part of a Rosetta stone for translation between mathematical "languages". I propose to explore the idea by, first, calculating the invariants (itself a difficult task) and, then, investigating their role in three other approaches to the same problem. I hope to work with leading teams in Canada, France and the US, and to help establish the UK as a leader in this exciting area.
Key Findings
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Organisation Website: http://www.shef.ac.uk