SEMICLASSICAL vs. EXACT SOLUTIONS OF CHARGED BLACK HOLE IN FOUR DIMENSIONS AND EXACT O(d, d) DUALITY

We derive a charged black hole solution in four dimensions described by SL(2, R)× SU(2)×U(1)/U(1)2 WZW coset model. Using the algebraic Hamiltonian method we calculate the corresponding solution that is exact 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 fulfil the cosmic censor conjecture, i.e. we find a naked singularity outside the black hole. Exact dual models are derived as well, one of them describes a 4D spacetime with a naked singularity. Using the algebraic Hamiltonian approach we also find the exact to all orders O(d, d) transformation of the metric and the dilaton field for general WZW coset models and show the correction with respect to the transformations in one loop order. 1 Work supported in part by the US-Israel Binational Science Foundation and the Israeli Academy of Sciences. † e-mail: [email protected]