Anti de Sitter space, squashed and stretched
Sep, 200525 pages
Published in:
- Class.Quant.Grav. 23 (2006) 971-986
e-Print:
- gr-qc/0509076 [gr-qc]
Report number:
- USITP-05-4
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Abstract: (arXiv)
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.- 04.20.-q
- 02.40.Hw
- space-time: anti-de Sitter
- dimension: 3
- causality
- horizon: Killing
- space: Weyl
- transformation: conformal
- black hole: Kerr
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