Alternatives to standard puncture initial data for binary black hole evolution

Standard puncture initial data have been widely used for numerical binary black hole evolutionsdespite their shortcomings, most notably the inherent lack of gravitational radiation at the initialtime that is later followed by a burst of spurious radiation. We study the evolution of three alterna-tive initial data schemes. Two of the three alternatives are based on post-Newtonian expansions thatcontain realistic gravitational waves. The first scheme is based on a second order post-Newtonianexpansion in Arnowitt, Deser, and Misner transverse-traceless (ADMTT) gauge that has been re-summed to approach standard puncture data at the black holes. The second scheme is based onasymptotic matching of the 4-metrics of two tidally perturbed Schwarzschild solutions to a first-order post-Newtonian expansion in ADMTT gauge away from the black holes. The final alternativeis obtained through asymptotic matching of the 4-metrics of two tidally perturbed Schwarzschildsolutions to a second-order post-Newtonian expansion in harmonic gauge away from the black holes.When evolved, the second scheme fails to produce quasicircular orbits (and instead leads to a nearlyhead-on collision). This failure can be traced back to inaccuracies in the extrinsic curvature dueto low-order matching. More encouraging is that the latter two alternatives lead to quasicircularorbits and show gravitational radiation from the onset of the evolution, as well as a reduction ofspurious radiation. Current deficiencies compared to standard punctures data include more eccen-tric trajectories during the inspiral and larger constraint violations, since the alternative data setsare only approximate solutions of Einstein’s equations. The eccentricity problem can be amelioratedby adjusting the initial momentum parameters.