Godel metric as a squashed anti-de Sitter geometry

Details Godel metric as a squashed anti-de Sitter geometry Godel metric as a squashed anti-de Sitter geometry

1998-04-09

arxiv.org/abs/gr-qc/9804027v2

Class.Quant.Grav. 15 (1998) 3241-3249

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

9 pages (LaTeX), 3 figures (EPS)

Scientific paper

10.1088/0264-9381/15/10/024

We show that the non flat factor of the Godel metric belongs to a one parameter family of 2+1 dimensional geometries that also includes the anti-de Sitter metric. The elements of this family allow a generalization a la Kaluza-Klein of the usual 3+1 dimensional Godel metric. Their lightcones can be viewed as deformations of the anti-de Sitter ones, involving tilting and squashing. This provides a simple geometric picture of the causal structure of these space-times, anti-de Sitter geometry appearing as the boundary between causally safe and causally pathological spaces. Furthermore, we construct a global algebraic isometric embedding of these metrics in 4+3 or 3+4 dimensional flat spaces, thereby illustrating in another way the occurrence of the closed timelike curves.

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