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Abstract
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Using the approach of the Poisson-Lie T-duality in the presence of spectators we first study the Abelian T-dualization of the BTZ black hole solution in such a way that our solution is in agreement with the solution obtained by Horowitz et al. Then, in order to study the non-Abelian T-duality of the BTZ black hole solution, we construct out a dual pair of sigma models related by Poisson-Lie symmetry so that the original model is built on a 2+1-dimensional manifold ℳ ≈ O× G in which G is a two-dimensional real non-Abelian Lie group that acts freely on ℳ and O is the orbit of G in ℳ. The findings of our study show that the original model indeed is canonically equivalent to the SL(2,ℜ) WZW model for a given value of the background parameters. In addition, by a convenient coordinate transformation we show that the original model describes a string propagating in a space-time with the BTZ black hole vacuum metric. The dual model is built on a 2+1-dimensional target manifold with two-dimensional real Abelian Lie group acting freely on it. Finally, we show that the dual model yields a new three-dimensional charged black string which is stationary and asymptotically flat.
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