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.

中文翻译：

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脉动相对论星的 Hamilton-Jacobi 流体动力学

自引力流体的动力学由偏微分方程的欧拉-爱因斯坦系统描述。流体 - 真空界面上适定性的破坏仍然是一个具有挑战性的开放性问题，这体现在振荡或激励双中子星的模拟中。我们制定并实施了一个适合于数值广义相对论中的中子星模拟的适定规范流体动力学方案。该方案使用 Carter-Lichnerowicz 的变分原理，说明正压流体运动是共形测地线，而亥姆霍兹第三定理说明最初的无旋流仍然是无旋的。我们将此方案应用于 3+1 数值广义相对论，以通过 Hamilton-Jacobi 方程演化流体元素的正则动量。我们探索了欧拉方程的正则化方案，该方案在流体静力平衡中使用基准气氛并允许压力消失，同时在真空边界上保持强双曲性。与标准的非平衡大气处理相比，新的正则化方案解决了更多的径向振荡模式。