Anti-de Sitter space, squashed and stretched

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 destroy 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.