Efficient Fully-Numerical Einstein-GRMHD Simulations in Curvilinear Coordinates

Here we describe techniques that we developed to efficiently evolved the Einstein Equations coupled to the equations for Magnetohydrodynamics in curvilinear coordinates. In particular, we focus on spherical coordinates and the challenges of producing accurate and efficient simulations in the presence of the coordinate singularities on the polar axis and the origin. As test cases, we present evolutions of stable and unstable magnetized rotating neutron stars, including collapse scenarios, as well as accurate simulations of gravitational waveforms.