Hamilton-Jacobi hydrodynamics of pulsating relativistic stars
arXiv:1912.03701 · doi:10.1088/1361-6382/ab93e9
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.
arXiv comment24 pgs, 3 figs. Typo fixed. v3: published version. https://doi.org/10.1088/1361-6382/ab93e9
References in corpus (26)
- SciPy 1.0--Fundamental Algorithms for Scientific Computing in Python
- Measuring the neutron star equation of state with gravitational wave observations
- Matter effects on binary neutron star waveforms
- Gravitational waves and nonaxisymmetric oscillation modes in mergers of compact object binaries
- Relativistic Magnetohydrodynamics In Dynamical Spacetimes: Numerical Methods And Tests
- Gravitational waves and mass ejecta from binary neutron star mergers: Effect of the mass-ratio
- Analytical representations of unified equations of state of neutron-star matter
- High-Order Fully General-Relativistic Hydrodynamics: new Approaches and Tests
- Well posedness for the motion of a compressible liquid with free surface boundary
- Binary Neutron Stars with Generic Spin, Eccentricity, Mass ratio, and Compactness - Quasi-equilibrium Sequences and First Evolutions
- Hydrodynamic Simulations in 3+1 General Relativity
- Irrotational Binary Neutron Stars in Quasiequilibrium in General Relativity
- Axisymmetric Modes of Rotating Relativistic Stars in the Cowling Approximation
- An introduction to relativistic hydrodynamics
- Frequency domain model of -mode dynamic tides in gravitational waveforms from compact binary inspirals
- An Introduction to Well-posedness and Free-evolution
- Characterizing the gamma-ray long-term variability of PKS 2155-304 with H.E.S.S. and Fermi-LAT
- Initial data for binary neutron stars with adjustable eccentricity
- Conservation of Circulation in Magnetohydrodynamics
- Revisiting Hyperbolicity of Relativistic Fluids
- Neutron star equation of state via gravitational wave observations
- Conservation laws and evolution schemes in geodesic, hydrodynamic and magnetohydrodynamic flows
- A priori estimates for relativistic liquid bodies
- Extended Kelvin theorem in relativistic magnetohydrodynamics
- Iteration Stability for Simple Newtonian Stellar Systems
- Lagrange coordinates for the Einstein-Euler equations