Gödel metric as a squashed anti-de Sitter geometry
M Rooman; Ph Spindel
Журнал:
Classical and Quantum Gravity
Дата:
1998-10-01
Аннотация:
We show that the non-flat factor of the Gödel 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 à la Kaluza-Klein of the usual (3 + 1)-dimensional Gödel 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 spacetimes, 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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