BSSN equations in spherical coordinates without regularization: Spherically symmetric spacetimes

Abstract

Brown recently introduced a covariant formulation of the BSSN equations which is well suited for curvilinear coordinate systems. This is particularly desirable as many astrophysical phenomena are symmetric with respect to the rotation axis or are such that curvilinear coordinates adapt better to their geometry. We show results from a newly developed numerical code solving the BSSN equations in spherical symmetry and the general relativistic hydrodynamic equations written in flux-conservative form. A key feature of the code is that uses a second-order partially implicit Runge-Kutta method to integrate the evolution equations, and does not need a regularization algorithm at the origin. We discuss a number of tests to assess the accuracy, numerical stability and expected convergence of the code.