Chiral geometries of (2+1)-d AdS gravity

Pure gravity in (2+1)-dimensions with negative cosmological constant is classically equivalent Chern-Simons gauge theory with gauge group SO(2,2), which may be realized on chiral and anti-chiral gauge connections. This Letter looks at half-AdS geometries i.e. those with a trivial right-moving gauge connection while the left-moving connection is a standard (Bañados-Teitelboim-Zanelli) BTZ connection. These are shown to be related by diffeomorphism to a BTZ geometry with different mass and angular momentum. Generically this is over-spinning, leading to a naked closed timelike curves. Other closely related solutions are also studied. These results suggest that the measure of the Chern-Simons path integral cannot factorize in a chiral way, if it is to represent a sum over physically sensible states.