Anti-de Sitter space, squashed and stretched

Abstract

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.

Asymptotic structure of topologically massive gravity in spacelike stretched AdS sector

“…The spacelike stretched black hole [5,6] is a particular solution of TMG Λ with several attractive features: it is a discrete quotient of the spacelike stretched AdS 3 vacuum (A.1), both solutions have the same type of asymptotic behaviour, and the corresponding black hole thermodynamics [15] seems to support the hypothesis made in [6], which "predicts" the existence of an asymptotic conformal symmetry in this sector of TMG Λ .…”

“…[3] introduced the so-called chiral version of the theory, defined by a specific relation between the coupling constants, and argued that it might lead to a consistent theory at both classical and quantum level [3,4]. Here, we follow another idea, related to the fact that TMG Λ has a rather rich vacuum structure [5,6]. Since the AdS sector of TMG Λ around AdS 3 is not consistent, Anninos et al [6] proposed to choose a new vacuum, the so-called spacelike stretched AdS 3 , which could be a stable ground state of the theory [7].…”

The Brown-York mass of black holes in Warped Anti-de Sitter space

“…This represents one of the most appealing attempts to generalize holography to non-AdS spaces, and this is because WAdS spaces appear in several contexts. For instance, WAdS spaces provide gravity duals for condensed matter systems with Schrödinger symmetry [12,13], they are closely related to the geometry of rotating black holes [14,15], and they also appear in relation to many other interesting subjects [16][17][18]. Asymptotically WAdS 3 spaces turn out to be exact solutions of String Theory [19][20][21][22][23] as well as of other models of threedimensional gravity, including Higher-Spin Gravity [24], Topologically Massive Gravity (TMG) [25,26], and New Massive Gravity (NMG) [27].…”

Rigid 4D N = 2 $$ \mathcal{N}=2 $$ supersymmetric backgrounds and actions

“…It is known that for any value of the stretching this space contains closed timelike curves. In particular, υ = 2 corresponds to Gödel spacetime [28,29].…”