T-duality and spinning solutions in 2 + 1 gravity

Starting with the 2 + 1 Einstein-Maxwell-Dilaton system with a cosmological constant and assuming two commuting Killing symmetries we derive the corresponding 1 + 0 σ-model. It is shown that, for general values of the coupling parameters, the T-duality group is SL(2, ℝ), which coincides with the group of linear coordinate transformations along the Killing orbits. This duality, along with a suitable parameter choice, is applied to obtain some new spinning solutions in the alternative gravity theories: Einstein-Maxwell, Brans-Dicke and Einstein-Maxwell-Dilaton.