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School of Mathematical Sciences

From computational fluid dynamics to gravitational wave observations

Supervisor: Dr Charalampos Markakis

Project description:

The dynamics of strongly gravitating fluid bodies is described by the Euler-Einstein system of partial differential equations, combining fluid dynamics with general relativity. Centuries after their advent, the solution to these equations remains mathematically and computationally difficult. The break-down of well-posedness on the fluid-vacuum interface remains a challenging open problem, which is manifested in simulations of binary neutron-star inspiral. The program will focus on formulating novel, well-posed canonical hydrodynamic schemes, suitable for inspiral simulations and gravitational-wave detection, with promising applications. The scheme uses a variational principle by Carter-Lichnerowicz stating that barotropic fluid motions are conformally geodesic, Helmholtz’s third theorem stating that initially irrotational flows remain irrotational, and Christodoulou's acoustic metric approach adopted to 3+1 numerical general relativity, to evolve the canonical momentum of a fluid element via Hamilton's equations. This work is made timely by the LIGO-Virgo detections of a double neutron star inspiral, the observation of electromagnetic counterparts for the first time, and the expected increase in sensitivity and rate of gravitational wave observations in the next years.

The proposed research is aimed at computationally exploring the theory of black holes and neutron stars, in order to improve our understanding of fundamental physical laws and reveal how nature operates on scales where our current understanding breaks down. As detectors improve their sensitivity and range, it is becoming increasingly important to invest in improving the accuracy of the waveform templates and reduce bias in astrophysical parameter estimation.

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