Regularity of the Einstein equations at future null infinity

Abstract

When Einstein's equations for an asymptotically flat, vacuum spacetime are reexpressed in terms of an appropriate conformal metric that is regular at (future) null infinity, they develop apparently singular terms in the associated conformal factor and thus appear to be ill-behaved at this (exterior) boundary. In this paper however we show, through an enforcement of the Hamiltonian and momentum constraints to the needed order in a Taylor expansion, that these apparently singular terms are not only regular at the boundary but can in fact be explicitly evaluated there in terms of conformally regular geometric data. Though we employ a rather rigidly constrained and gauge-fixed formulation of the field equations, we discuss the extent to which we expect our results to have a more ‘universal’ significance and, in particular, to be applicable, after minor modifications, to alternative formulations.