Towards the solution of the relativistic gravitational radiation reaction problem for binary black holes

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Abstract
Here we present the results of applying the generalized Riemann ζ-function regularization method to the gravitational radiation reaction problem. We analyse in detail the head-on collision of two non-spinning black holes with an extreme mass ratio. The resulting reaction force on the smaller hole is repulsive. We discuss the possible extensions of these method to generic orbits and spinning black holes. The determination of corrected trajectories allows us to add second perturbative corrections with the consequent increase in the accuracy of computed waveforms.