Three-dimensional general relativistic hydrodynamics II: long-term dynamics of single relativistic stars

TL;DR

This paper presents a highly accurate 3D general relativistic hydrodynamics code for simulating the long-term evolution of relativistic stars, including new physics results and eigenfrequency calculations for rotating stars.

Contribution

The paper introduces a novel 3D code with advanced spacetime evolution and shock capturing techniques, enabling precise long-term simulations and eigenfrequency determination of rotating relativistic stars.

Findings

Most accurate long-term 3D evolutions of relativistic stars to date

First eigenfrequencies of rotating stars in full general relativity

Validation of new numerical methods against previous approaches

Abstract

This is the second in a series of papers on the construction and validation of a three-dimensional code for the solution of the coupled system of the Einstein equations and of the general relativistic hydrodynamic equations, and on the application of this code to problems in general relativistic astrophysics. In particular, we report on the accuracy of our code in the long-term dynamical evolution of relativistic stars and on some new physics results obtained in the process of code testing. The tests involve single non-rotating stars in stable equilibrium, non-rotating stars undergoing radial and quadrupolar oscillations, non-rotating stars on the unstable branch of the equilibrium configurations migrating to the stable branch, non-rotating stars undergoing gravitational collapse to a black hole, and rapidly rotating stars in stable equilibrium and undergoing quasi-radial oscillations. The numerical evolutions have been carried out in full general relativity using different types of polytropic equations of state using either the rest-mass density only, or the rest-mass density and the internal energy as independent variables. New variants of the spacetime evolution and new high resolution shock capturing (HRSC) treatments based on Riemann solvers and slope limiters have been implemented and the results compared with those obtained from previous methods. Finally, we have obtained the first eigenfrequencies of rotating stars in full general relativity and rapid rotation. A long standing problem, such frequencies have not been obtained by other methods. Overall, and to the best of our knowledge, the results presented in this paper represent the most accurate long-term three-dimensional evolutions of relativistic stars available to date.