Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
1995-03-06
Phys.Rev. D52 (1995) 2020-2029
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
25 pages, LaTex
Scientific paper
10.1103/PhysRevD.52.2020
We consider 1 spacelike Killing vector field reductions of 4-d vacuum general relativity. We restrict attention to cases in which the manifold of orbits of the Killing field is $R^{3}$. The reduced Einstein equations are equivalent to those for Lorentzian 3-d gravity coupled to an SO(2,1) nonlinear sigma model on this manifold. We examine the theory in terms of a Hamiltonian formulation obtained via a 2+1 split of the 3-d manifold. We restrict attention to geometries which are asymptotically flat in a 2-d sense defined recently. We attempt to pass to a reduced Hamiltonian description in terms of the true degrees of freedom of the theory via gauge fixing conditions of 2-d conformal flatness and maximal slicing. We explicitly solve the diffeomorphism constraints and relate the Hamiltonian constraint to the prescribed negative curvature equation in $R^2$ studied by mathematicians. We partially address issues of existence and/or uniqueness of solutions to the various elliptic partial differential equations encountered.
No associations
LandOfFree
On the gauge fixing of 1 Killing field reductions of canonical gravity: the case of asymptotically flat induced 2-geometry 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 On the gauge fixing of 1 Killing field reductions of canonical gravity: the case of asymptotically flat induced 2-geometry, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On the gauge fixing of 1 Killing field reductions of canonical gravity: the case of asymptotically flat induced 2-geometry will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-285341