%0 Journal Article
%T On the stability of solutions of the Lichnerowicz-York equation
%A Darragh M Walsh
%J Physics
%D 2012
%I arXiv
%R 10.1088/0264-9381/30/6/065007
%X We study the stability of solution branches for the Lichnerowicz-York equation at moment of time symmetry with constant unscaled energy density. We prove that the weak-field lower branch of solutions is stable whilst the upper branch of strong-field solutions is unstable. The existence of unstable solutions is interesting since a theorem by Sattinger proves that the sub-super solution monotone iteration method only gives stable solutions.
%U http://arxiv.org/abs/1210.4950v2