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Paper   IPM / Physic / 11502
School of Physics
  Title:   Orientifolded Locally AdS3 Geometries
  Author(s): 
1.  F. Loran
2.  M.M. Sheikh-Jabbari
  Status:   Published
  Journal: Classical Quant. Grav.
  Vol.:  28
  Year:  2011
  Pages:   025013
  Supported by:  IPM
  Abstract:
Continuing the analysis of [arXiv:1003.4089[hep-th]], we classify all locally AdS3 stationary axi-symmetric unorientable solutions to AdS3 Einstein gravity and show that they are obtained by applying certain orientifold projection on AdS3, BTZ or AdS3 self-dual orbifold, respectively O-AdS3, O-BTZ and O-SDO geometries. Depending on the orientifold fixed surface, the O-surface, which is either a space-like 2D plane or cylinder, or a light-like 2D plane or cylinder one can distinguish four distinct cases. For the space-like orientifold plane or cylinder cases these geometries solve AdS3 Einstein equations and are hence locally AdS3 everywhere except at the at O-surface, where there is a delta-function source. For the light-like cases the geometry is solution to Einstein equations even at the O-surface. We discuss the causal structure for static, extremal and general rotating O-BTZ and O-SDO cases as well as the geodesic motion on these geometries. We also discuss orientifolding Poincaré patch AdS3 and AdS2 geometries as a way to geodesic completion of these spaces and comment on the 2D CFT dual to the O-geometries.

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