Numerical Relativity in Spherical Polar Coordinates: Off-center Simulations

TL;DR

This paper introduces a new numerical relativity approach in spherical polar coordinates that handles off-center simulations, including black holes and neutron stars, without regularization or symmetry assumptions, and demonstrates its effectiveness through various complex tests.

Contribution

The paper presents a novel reference-metric formulation for numerical relativity in spherical coordinates that enables off-center and asymmetric simulations without regularization or symmetry assumptions.

Findings

Successfully simulated off-center black holes and neutron stars.

Demonstrated stable evolution of shock waves through the coordinate origin.

Validated the approach with complex asymmetric collision scenarios.

Abstract

We have recently presented a new approach for numerical relativity simulations in spherical polar coordinates, both for vacuum and for relativistic hydrodynamics. Our approach is based on a reference-metric formulation of the BSSN equations, a factoring of all tensor components, as well as a partially implicit Runge-Kutta method, and does not rely on a regularization of the equations, nor does it make any assumptions about the symmetry across the origin. In order to demonstrate this feature we present here several off-centered simulations, including simulations of single black holes and neutron stars whose center is placed away from the origin of the coordinate system, as well as the asymmetric head-on collision of two black holes. We also revisit our implementation of relativistic hydrodynamics and demonstrate that a reference-metric formulation of hydrodynamics together with a factoring of all tensor components avoids problems related to the coordinate singularities at the origin and on the axes. As a particularly demanding test we present results for a shock wave propagating through the origin of the spherical polar coordinate system.