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 multipoles to show that all -metric coefficients are at the location of the particle. Summing over , to reconstruct the full metric, gives a formally divergent result. We succeed in bringing this sum to a Riemann's -function regularization scheme and numerically compute the first-order geodesics.
- Received 8 October 1999
DOI:https://doi.org/10.1103/PhysRevLett.84.5251
©2000 American Physical Society