Numerical relativity in spherical polar coordinates: Off-center simulations

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 Baumgarte-Shapiro-Shibata-Nakamura 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.