Space-times admitting a three-dimensional conformal group

Details Space-times admitting a three-dimensional conformal group Space-times admitting a three-dimensional conformal group

2000-05-16

arxiv.org/abs/gr-qc/0005070v1

Gen.Rel.Grav. 28 (1996) 311-337

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

Latex 34 pages

Scientific paper

Perfect fluid space-times admitting a three-dimensional Lie group of conformal motions containing a two-dimensional Abelian Lie subgroup of isometries are studied. Demanding that the conformal Killing vector be proper (i.e., not homothetic nor Killing), all such space-times are classified according to the structure of their corresponding three-dimensional conformal Lie group and the nature of their corresponding orbits (that are assumed to be non-null). Each metric is then explicitly displayed in coordinates adapted to the symmetry vectors. Attention is then restricted to the diagonal case, and exact perfect fluid solutions are obtained in both the cases in which the fluid four-velocity is tangential or orthogonal to the conformal orbits, as well as in the more general "tilting" case.

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