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Physics  2012 

On the stability of solutions of the Lichnerowicz-York equation

DOI: 10.1088/0264-9381/30/6/065007

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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.

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