Quasistationary binary inspiral. I. Einstein equations for the two Killing vector spacetime

The inspiral of a binary system of compact objects due to gravitational radiation 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 model are used, according to a formalism introduced by Geroch, to describe the 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 equations for the toy model spacetime are derived in terms of the degrees of freedom which remain after a particular choice of gauge.