A Fully General Relativistic Numerical Simulation Code for Spherically Symmetric Matter

Abstract

We present a fully general relativistic open-source code that can be used for simulating a system of spherically symmetric perfect fluid matter. It is based on the Arnowitt-Deser-Misner 3+1 formalism with maximal slicing and isotropic spatial coordinates. For hydrodynamic matter High Resolution Shock Capturing (HRSC) schemes with a monotonized central-difference limiter and approximated Riemann solvers are used in the Eulerian viewpoint. The accuracy and the convergence of our numerical code are verified by performing several test problems. These include a relativistic blast wave, relativistic spherical accretion of matter into a black hole, Tolman-Oppenheimer-Volkoff (TOV) stars and Oppenheimer-Snyder (OS) dust collapses. In particular, a dynamical code test is done for the OS collapse by explicitly performing numerical coordinate transformations between our coordinate 8system and the one used for the analytic solution. Finally, some TOV star solutions are presented for the Eddington-inspired Born-Infeld gravity theory.