Radiation content of Conformally flat initial data

Abstract

We study the radiation of energy and linear momentum emitted to infinity by the headon collision of binary black holes, starting from rest at a finite initial separation, in the extreme mass ratio limit. For these configurations we identify the radiation produced by the initially conformally flat choice of the three geometry. This identification suggests that the radiated energy and momentum of headon collisions will not be dominated by the details of the initial data for evolution of holes from initial proper separations $L_0\geq7M$. For non-headon orbits, where the amount of radiation is orders of magnitude larger, the conformally flat initial data may provide a relative even better approximation.