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 $1+0 \sigma$--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.