SEMICLASSICAL VERSUS EXACT-SOLUTIONS OF CHARGED BLACK-HOLE IN 4 DIMENSIONS AND EXACT O(D, D) DUALITY

We derive a charged black hole solution in four dimensions described b y SL(2, R) x SU(2) X U(1)/U(1)2 WZW coset model. Using the algebraic h amiltonian method we calculate the corresponding solution that is exac t to all orders in 1/k. It is shown that unlike the 2D black hole, the singularity remains also in the exact solution, and moreover, in some range of the gauge parameter the space-time does not fulfill the cosm ic censor conjecture, i.e. we find a naked singularity outside the bla ck hole. Exact dual models are derived as well, one of them describes a 4D space-time with a naked singularity. Using the algebraic hamilton ian approach we also find the exact to all orders O(d, d) transformati on of the metric and the dilaton field for general WZW coset models an d show the correction with respect to the transformations in one-loop order.