https://doi.org/10.1140/epjc/s10052-016-4326-z
Regular Article - Theoretical Physics
On 3d bulk geometry of Virasoro coadjoint orbits: orbit invariant charges and Virasoro hair on locally AdS
geometries
1
School of Physics, Institute for Research in Fundamental Sciences (IPM), P.O.Box 19395-5531, Tehran, Iran
2
State Key Laboratory of Theoretical Physics, Institute of Theoretical Physics, Chinese Academy of Sciences, Beijing, 100190, China
* e-mail: yavar@itp.ac.cn
Received:
29
June
2016
Accepted:
18
August
2016
Published online:
8
September
2016
Expanding upon [arXiv:1404.4472, arXiv:1511.06079], we provide a further detailed analysis of Bañados geometries, the most general solutions to the AdS Einstein gravity with Brown–Henneaux boundary conditions. We analyze in some detail the causal, horizon, and boundary structure, and the geodesic motion on these geometries, as well as the two classes of symplectic charges one can associate with these geometries: charges associated with the exact symmetries and the Virasoro charges. We elaborate on the one-to-one relation between the coadjoint orbits of two copies of the Virasoro group and Bañados geometries. We discuss that the information as regards the Bañados goemetries falls into two categories: “orbit invariant” information and “Virasoro hairs”. The former concerns geometric quantities, while the latter are specified by the non-local surface integrals. We elaborate on multi-BTZ geometries which have a 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 AdS Einstein gravity.
© The Author(s), 2016
