  Expanding upon [arXiv:1404.4472, 1511.06079], we provide further detailed
analysis of Ba\~nados 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 the
coadjoint orbits of two copies of Virasoro group and Ba\~nados geometries. We
discuss that the information about the Ba\~nados goemetries fall into two
categories: "orbit 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.
