Hamilton-Jacobi hydrodynamics of pulsating relativistic stars

John Ryan Westernacher-Schneider, Charalampos Markakis, Bing Jyun Tsao

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish (US)
Article number155005
JournalClassical and Quantum Gravity
Issue number15
StatePublished - Aug 6 2020


  • Hamilton-Jacobi formulation
  • hydrodynamics
  • numerical relativity

ASJC Scopus subject areas

  • Physics and Astronomy (miscellaneous)


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