Anti-de Sitter space, squashed and stretched

Details Anti-de Sitter space, squashed and stretched Anti-de Sitter space, squashed and stretched

2005-09-20

arxiv.org/abs/gr-qc/0509076v2

Class.Quant.Grav.23:971-986,2006

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

25 pages, 2 figures; oversight corrected

Scientific paper

10.1088/0264-9381/23/3/022

We study the Lorentzian analogues of the squashed 3-sphere, namely 2+1 dimensional anti-de Sitter space, squashed or stretched along fibres that are either spacelike or timelike. The causal structure, and the property of being an Einstein--Weyl space, depend critically on whether we squash or stretch. We argue that squashing, and stretching, completely destroys the conformal boundary of the unsquashed spacetime. As a physical application we observe that the near horizon geometry of the extremal Kerr black hole, at constant Boyer--Lindquist latitude, is anti-de Sitter space squashed along compactified spacelike fibres.

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