Axisymmetric general relativistic hydrodynamics: Long-term evolution of neutron stars and stellar collapse to neutron stars and black holes

摘要

We report a new implementation for axisymmetric simulation in full generalrelativity. In this implementation, the Einstein equations are solved using theNakamura-Shibata formulation with the so-called cartoon method to impose anaxisymmetric boundary condition, and the general relativistic hydrodynamicequations are solved using a high-resolution shock-capturing scheme based on anapproximate Riemann solver. As tests, we performed the following simulations:(i) long-term evolution of non-rotating and rapidly rotating neutron stars,(ii) long-term evolution of neutron stars of a high-amplitude dampingoscillation accompanied with shock formation, (iii) collapse of unstableneutron stars to black holes, and (iv) stellar collapses to neutron stars. Thetests (i)--(iii) were carried out with the $\Gamma$-law equation of state, andthe test (iv) with a more realistic parametric equation of state forhigh-density matter. We found that this new implementation works very well: Itis possible to perform the simulations for stable neutron stars for more than10 dynamical time scales, to capture strong shocks formed at stellar corecollapses, and to accurately compute the mass of black holes formed after thecollapse and subsequent accretion. In conclusion, this implementation is robustenough to apply to astrophysical problems such as stellar core collapse ofmassive stars to a neutron star and black hole, phase transition of a neutronstar to a high-density star, and accretion-induced collapse of a neutron starto a black hole. The result for the first simulation of stellar core collapseto a neutron star started from a realistic initial condition is also presented.