Inertia (Mechanics)

We study the evolution of binary black hole initial data schemes as alternatives to the standard puncture construction. These alternatives are based on post-Newtonian expansions that contain realistic gravitational waves. The first scheme is based on a second order post-Newtonian expansion in Arnowitt, Deser, and Misner transverse-traceless (ADMTT) gauge that has been re-summed to approach standard puncture data at the black holes. The other schemes are based on asymptotic matching of the 4-metrics of two tidally perturbed Schwarzschild solutions to post-Newtonian expansions at different orders. The alternatives are encouraging and lead to quasi-circular orbits and show gravitational radiation from the onset, as well as a reduction of spurious radiation. Deficiencies compared to punctures include more eccentricity during inspiral and larger constraint violations, since the alternative data sets only approximate solutions of Einstein's equations.