Hypersurface-orthogonal generators of an orthogonally transitive transitive $G_2I$, topological identifications, and axially and cylindrically symmetric spacetimes

Details Hypersurface-orthogonal generators of an orthogonally transitive transitive $G_2I$, topological identifications, and axially and cylindrically symmetric spacetimes Hypersurface-orthogonal generators of an orthogonally transitive transitive $G_2I$, topological identifications, and axially and cylindrically symmetric spacetimes

1997-10-03

arxiv.org/abs/gr-qc/9710024v1

Gen.Rel.Grav.30:131-150,1998

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

16 pages, latex 2.09, no figures. Accepted for publication in General Relativity and Gravitation

Scientific paper

10.1023/A:1018833219068

A criterion given by Castejon-Amenedo and MacCallum (1990) for the existence of (locally) hypersurface-orthogonal generators of an orthogonally-transitive two-parameter Abelian group of motions (a $G_2I$) in spacetime is re-expressed as a test for linear dependence with constant coefficients between the three components of the metric in the orbits in canonical coordinates. In general, it is shown that such a relation implies that the metric is locally diagonalizable in canonical coordinates, or has a null Killing vector, or can locally be written in a generalized form of the `windmill' solutions characterized by McIntosh. If the orbits of the $G_2I$ have cylindrical or toroidal topology and a periodic coordinate is used, these metric forms cannot in general be realized globally as they would conflict with the topological identification. The geometry then has additional essential parameters, which specify the topological identification. The physical significance of these parameters is shown by their appearance in global holonomy and by examples of exterior solutions where they have been related to characteristics of physical sources. These results lead to some remarks about the definition of cylindrical symmetry.

Affiliated with

Also associated with

No associations

Rating

Hypersurface-orthogonal generators of an orthogonally transitive transitive $G_2I$, topological identifications, and axially and cylindrically symmetric spacetimes 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 Hypersurface-orthogonal generators of an orthogonally transitive transitive $G_2I$, topological identifications, and axially and cylindrically symmetric spacetimes, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Hypersurface-orthogonal generators of an orthogonally transitive transitive $G_2I$, topological identifications, and axially and cylindrically symmetric spacetimes will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-142926