Non-uniqueness in conformal formulations of the Einstein constraints

Details Non-uniqueness in conformal formulations of the Einstein constraints Non-uniqueness in conformal formulations of the Einstein constraints

2006-10-26

arxiv.org/abs/gr-qc/0610129v2

Class.Quant.Grav.24:1911-1926,2007

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

Arguments clarified and typos corrected. Matches published version

Scientific paper

10.1088/0264-9381/24/8/002

Standard methods in non-linear analysis are used to show that there exists a parabolic branching of solutions of the Lichnerowicz-York equation with an unscaled source. We also apply these methods to the extended conformal thin sandwich formulation and show that if the linearised system develops a kernel solution for sufficiently large initial data then we obtain parabolic solution curves for the conformal factor, lapse and shift identical to those found numerically by Pfeiffer and York. The implications of these results for constrained evolutions are discussed.

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