$O(\tilde d,\tilde d)$ Transformations and 3D Black Hole

We generalize the results of a previous paper by one of the authors to show a relationship among a class of string solutions through $O(\tilde d, \tilde d)$ transformations. The results are applied to a rotating black hole solution of three dimensional general relativity discussed recently. We extend the black hole solution to string theory and show its connection with the three dimensional black string with nonzero momentum through an $O(\tilde d, \tilde d)$ transformation of the above type.

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