Constraint equations for 3+1 vacuum Einstein equations with a translational space-like Killing field in the asymptotically flat case II

Article type: Research Article

Authors: Huneau, Cécile

Affiliations: DPMMS, Centre for Mathematical Sciences, Wilberforce Road, Cambridge CB3 0WB, UK. E-mail: cecile.huneau@ens.fr

Abstract: We solve the Einstein constraint equations for a (3+1)-dimensional vacuum space–time with a space-like translational Killing field in the asymptotically flat case. The presence of a space-like translational Killing field allows for a reduction of the (3+1)-dimensional problem to a (2+1)-dimensional one. The aim of this paper is to go further in the asymptotic expansion of the solutions than in [Constraint equations for 3+1 vacuum Einstein equations with a translational space-like Killing field in the asymptotically flat case, available at: arXiv:1302.1473]. In particular the expansion we construct involves quantities which are the 2-dimensional equivalent of the global charges.

Keywords: general relativity, Einstein constraint equations, asymptotic flatness

DOI: 10.3233/ASY-151333

Journal: Asymptotic Analysis, vol. 96, no. 1, pp. 51-89, 2016