Asymptotically flat vacuum initial data sets from a modified parabolic-hyperbolic formulation of the Einstein vacuum constraint equations

Abstract

In this paper we continue earlier investigations [F. Beyer et al., Classical Quantum Gravity 34, 205014 (2017)CQGRDG0264-938110.1088/1361-6382/aa8be6; F. Beyer et al., Classical Quantum Gravity 36, 175005 (2019)CQGRDG0264-938110.1088/1361-6382/ab3482; K. Csukás and I. Rácz, arXiv:1911.02900] of evolutionary formulations of the Einstein vacuum constraint equations originally introduced by Rácz. Motivated by the strong evidence from these works that the resulting vacuum initial data sets are generically not asymptotically flat we analyze the asymptotics of the solutions of a modified formulation by a combination of analytical and numerical techniques. We conclude that the vacuum initial data sets generated with this new formulation are generically asymptotically flat.