1210.4950 (Darragh M Walsh)

On the stability of solutions of the Lichnerowicz-York equation    [PDF]

Darragh M Walsh

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 convergence method only gives stable solutions.

View original: http://arxiv.org/abs/1210.4950