Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
1993-09-09
Phys.Rev. D49 (1994) 2792-2800
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
25 pages, preprint YCTP-20-93, Revtex
Scientific paper
10.1103/PhysRevD.49.2792
We show that for $U(1)$-symmetric spacetimes on $S^3 \times R$ a constant of motion associated with the well known Geroch transformation, a functional $K[h_{ij},\pi^{ij}]$, quadratic in gravitational momenta, is strictly positive in an open subset of the set of all $U(1)$-symmetric initial data, and therefore not weakly zero. The Mixmaster initial data appear to be on the boundary of that set. We calculate the constant of motion perturbatively for the Mixmaster spacetime and find it to be proportional to the minisuperspace Hamiltonian to the first order in the Misner anisotropy variables, i.e. weakly zero. Assuming that $K$ is exactly zero for the Mixmaster spacetime, we show that Geroch's transformation, when applied to the Mixmaster spacetime, gives a new \mbox{$U(1)$-symmetric} solution of the vacuum Einstein equations, globally defined on \mbox{$S^2 \times S^1 \times R$},which is non-homogeneous and presumably exhibits Mixmaster-like complicated dynamical behavior.
Grubisic Boro
Moncrief Vincent
No associations
LandOfFree
The Mixmaster Spacetime, Geroch's Transformation and Constants of Motion 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 The Mixmaster Spacetime, Geroch's Transformation and Constants of Motion, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and The Mixmaster Spacetime, Geroch's Transformation and Constants of Motion will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-380454