Godel metric as a squashed anti-de Sitter geometry

Rooman, M.; Spindel, P.

doi:10.1088/0264-9381/15/10/024

Godel metric as a squashed anti-de Sitter geometry

M. Rooman
(
- Brussels U.
)
,
P. Spindel
(
- UMH, Mons
)

Apr, 1998

8 pages

Published in:

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

e-Print:

gr-qc/9804027 [gr-qc]

DOI:

10.1088/0264-9381/15/10/024

Report number:

UMH-MG-98-01,
ULB-TH-98-06

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Abstract: (arXiv)

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.