Quasistationary binary inspiral. I. Einstein equations for the two Killingvector spacetime - art. no. 084009

The inspiral of a binary system of compact objects due to gravitational rad iation is investigated using the toy model of two infinitely long lines of mass moving in a fixed circular orbit. The two Killing fields in the toy mo del are used, according to a formalism introduced by Geroch, to describe th e geometry entirely in terms of a set of tensor fields on the two-manifold of Killing vector orbits. Geroch's derivation of the Einstein equations in this formalism is streamlined and generalized. The explicit Einstein equati ons for the toy model spacetime are derived in terms of the degrees of free dom which remain after a particular choice of gauge. [S0556-2821(99)05618-0 ].