Computation of the conformal algebra of 1+3 decomposable spacetimes

Details Computation of the conformal algebra of 1+3 decomposable spacetimes Computation of the conformal algebra of 1+3 decomposable spacetimes

1998-10-30

arxiv.org/abs/gr-qc/9810088v1

Class.Quant.Grav. 15 (1998) 2909-2921

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

15 pages Latex, no figures. Minor mistakes corrected

Scientific paper

10.1088/0264-9381/15/9/032

The conformal algebra of a 1+3 decomposable spacetime can be computed from the conformal Killing vectors (CKV) of the 3-space. It is shown that the general form of such a 3-CKV is the sum of a gradient CKV and a Killing or homothetic 3-vector. It is proved that spaces of constant curvature always admit such conformal Killing vectors. As an example, the complete conformal algebra of a G\"odel-type spacetime is computed. Finally it is shown that this method can be extended to compute the conformal algebra of more general non-decomposable spacetimes.

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