English

On the stability of solutions of the Lichnerowicz-York equation

General Relativity and Quantum Cosmology 2015-06-11 v2

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.

Keywords

Cite

@article{arxiv.1210.4950,
  title  = {On the stability of solutions of the Lichnerowicz-York equation},
  author = {Darragh M Walsh},
  journal= {arXiv preprint arXiv:1210.4950},
  year   = {2015}
}

Comments

To appear in Classical and Quantum Gravity