Kelvin's theorem and Hamilton-Jacobi fluid theory in gravitational wave astrophysics

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• Charalampos Markakis (University of Cambridge)
• Friday 15 February 2019, 13:00-14:00
• Pavilion B Potter Room (B1.19).

If you have a question about this talk, please contact Nathan Johnson-McDaniel.

The motion of strongly gravitating fluid bodies is described by the Euler-Einstein system of partial differential equations. Centuries after their advent, the solution to these equations remains mathematically and computationally difficult, and the break-down of well-posedness on the boundary interface between fluid and vacuum remains a challenging open problem. The problem manifests itself in numerical simulations of binary neutron-star inspiral. This talk focuses on formulating and implementing well-posed, acoustical and canonical hydrodynamic schemes, suitable for inspiral simulations and gravitational-wave source modelling. The scheme uses a variational principle by Carter-Lichnerowicz stating that barotropic fluid motions are conformally geodesic, a corollary to Kelvin’s theorem stating that initially irrotational flows remain irrotational, and Christodoulou’s acoustic metric approach adopted to numerical relativity, in order to evolve the canonical momentum of a fluid element via Hamilton’s equations. These mathematical theorems leave their fingerprints on inspiral waveforms from binary neutron stars observed by the LIGO and Virgo detectors.

This talk is part of the DAMTP Friday GR Seminar series.

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