Computation of the conformal algebra of 1+3 decomposable spacetimes

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 ad...

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Bibliographic Details
Published in:arXiv.org 1998-10
Main Authors: Tsamparlis, Michael, Nikolopoulos, Dimitris, Apostolopoulos, Pantelis S
Format: Article
Language:English
Subjects:
Algebra
Computation
Curvature
Decomposition
Mathematical analysis
Spacetime
Vectors (mathematics)
Online Access:Get full text
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Summary: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.
ISSN:2331-8422
DOI:10.48550/arxiv.9810088