Black hole head-on collisions and gravitational waves with fixed mesh-refinement and dynamic singularity excision

Abstract

We present long-term-stable and convergent evolutions of head-on black-hole collisions and extraction of gravitational waves generated during the merger and subsequent ring-down. The new ingredients in this work are the use of fixed mesh-refinement and dynamical singularity excision techniques. We are able to carry out head-on collisions with large initial separations and demonstrate that our excision infrastructure is capable of accommodating the motion of the individual black holes across the computational domain as well as their merger. We extract gravitational waves from these simulations using the Zerilli-Moncrief formalism and find the ring-down radiation to be, as expected, dominated by the $\ensuremath{\ell}=2$, $m=0$ quasinormal mode. The total radiated energy is about $0.1%$ of the total Arnowitt-Deser-Misner mass of the system.