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arXiv · 1210.4950

On the stability of solutions of the Lichnerowicz-York equation

Darragh M Walsh
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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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Darragh M Walsh. 2013-02-07. On the stability of solutions of the Lichnerowicz-York equation. https://doi.org/10.1088/0264-9381%2F30%2F6%2F065007

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