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arXiv · 1912.03701

Hamilton-Jacobi hydrodynamics of pulsating relativistic stars

John Ryan Westernacher-Schneider·Charalampos Markakis·Bing Jyun Tsao
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Abstract

The dynamics of self-gravitating fluid bodies is described by the Euler-Einstein system of partial differential equations. The break-down of well-posedness on the fluid-vacuum interface remains a challenging open problem, which is manifested in simulations of oscillating or inspiraling binary neutron-stars. We formulate and implement a well-posed canonical hydrodynamic scheme, suitable for neutron-star simulations in numerical general relativity. The scheme uses a variational principle by Carter-Lichnerowicz stating that barotropic fluid motions are conformally geodesic and Helmholtz's third theorem stating that initially irrotational flows remain irrotational. We apply this scheme in 3+1 numerical general relativity to evolve the canonical momentum of a fluid element via the Hamilton-Jacobi equation. We explore a regularization scheme for the Euler equations, that uses a fiducial atmosphere in hydrostatic equilibrium and allows the pressure to vanish, while preserving strong hyperbolicity on the vacuum boundary. The new regularization scheme resolves a larger number of radial oscillation modes compared to standard, non-equilibrium atmosphere treatments.

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John Ryan Westernacher-Schneider, Charalampos Markakis, Bing Jyun Tsao. 2019-12-08. Hamilton-Jacobi hydrodynamics of pulsating relativistic stars. https://doi.org/10.1088/1361-6382%2Fab93e9

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