Binary black hole spacetimes with a helical Killing vector in a projection formalism

Abstract

Binary black hole spacetimes with a helical Killing vector are discussed as an approximation for the early stage of a binary system. The Einstein equations are studied in a projection formalism for this case where they are equivalent to a three dimensional gravitational theory with an SL(2, C)/SO(1, 1) sigma model as the material source. 2 + 1 decompositions of the 3‐metric are used to establish the field equations on the orbit space of the Killing vector. The Killing horizons and the light cylinder are shown to be regular singularities, i.e., the metric functions can be expanded in a formal power series in the vicinity. It is shown that the spacetime cannot be asymptotically flat in the strong sense to have a smooth null infinity.