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Paper   IPM / Physic / 14311
School of Physics
  Title:   On 3d Bulk Geometry of Virasoro Coadjoint Orbits: Orbit invariant charges and Virasoro hair on locally AdS3 geometries
1.  M.M. Sheikh-Jabbari
2.  H. Yavartanoo
  Status:   Published
  Journal: Eur. Phys. J. C
  No.:  9
  Vol.:  76
  Year:  2016
  Pages:   493
  Supported by:  IPM
Expanding upon [arXiv:1404.4472, 1511.06079], we provide further detailed analysis of Banados geometries, the most general solutions to the AdS3 Einstein gravity with Brown-Henneaux boundary conditions. We analyze in some detail the causal, horizon and boundary structure, and geodesic motion on these geometries, as well as the two class of symplectic charges one can associate with these geometries: charges associated with the exact symmetries and the Virasoro charges. We elaborate further the one-to-one relation between representations of two copies of Virasoro group (Virasoro coadjoint orbits) and Banados geometries. We discuss that the information about the Banados goemetries fall into two categories: örbit invariant" information and "Virasoro hairs". The former are geometric quantities while the latter are specified by the non-local surface integrals. We elaborate on multi-BTZ geometries which have some number of disconnected pieces at the horizon bifurcation curve. We study multi-BTZ black hole thermodynamics and discuss that the thermodynamic quantities are orbit invariants. We also comment on the implications of our analysis for a 2d CFT dual which could possibly be dual to AdS3 Einstein gravity.

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