title: Pragmatic approach to gravitational radiation reaction in binary black holes
abstract: We study the relativistic orbit of binary black holes in systems with small mass ratio. The trajectory of the smaller object (another black hole or a neutron star), represented as a particle, is determined by the geodesic equation on the perturbed massive black hole spacetime. Here we study perturbations around a Schwarzschild black hole using Moncrief's gauge invariant formalism. We decompose the perturbations into l multipoles to show that all l-metric coefficients are C0 at the location of the particle. Summing over l, to reconstruct the full metric, gives a formally divergent result. We succeed in bringing this sum to a Riemann's zeta-function regularization scheme and numerically compute the first-order geodesics.
authors.affiliation: Max-Planck-Institut fur Gravitationsphysik, Albert-Einstein-Institut, Am Muhlenberg 1, D-14476 Golm, Germany, and Instituto de Astronomia y Fisica del Espacio-CONICET, Buenos Aires, Argentina.
authors.initials: CO
authors.lastname: Lousto