Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
2005-02-11
Acta Phys.Polon. B36 (2005) 109-120
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
12 pages
Scientific paper
James York, in a major extension of Andr\'e Lichnerowicz's work, showed how to construct solutions to the constraint equations of general relativity. The York method consists of choosing a 3-metric on a given manifold; a divergence-free, tracefree (TT) symmetric 2-tensor wrt this metric; and a single number, the trace of the extrinsic curvature. One then obtains a quasi-linear elliptic equation for a scalar function, the Lichnerowicz-York (L-Y) equation. The solution of this equation is used as a conformal factor to transform the data into a set that satisfies the constraints. If the manifold is compact and without boundary, one quantity that emerges is the volume of the physical space. This article reinterprets the L-Y equation as an eigenvalue equation so as to get a set of data with a preset physical volume. One chooses the conformal metric, the TT tensor, and the physical volume, while regarding the trace of the extrinsic curvature as a free parameter. The resulting equation has extremely nice uniqueness and existence properties. A even more radical approach would be to fix the base (conformal) metric, the physical volume, and the trace. One also selects a TT tensor, but one is free to multiply it by a constant(unspecified). One then solves the L-Y equation as an eigenvalue equation for this constant. A third choice would be to fix the TT tensor and and multiply the base metric by a constant. Each of these three formulations has good uniqueness and existence properties.
No associations
LandOfFree
Readings of the Lichnerowicz-York equation does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Readings of the Lichnerowicz-York equation, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Readings of the Lichnerowicz-York equation will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-54815