On the stability of solutions of the Lichnerowicz-York equation
arXiv:1210.4950 · doi:10.1088/0264-9381/30/6/065007
Abstract
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.
To appear in Classical and Quantum Gravity
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