Conformally Exact Results for SL(2,R)\times SO(1,1)^{d-2}/SO(1,1) Coset Models

Using the conformal invariance of the $SL(2,R)\otimes SO(1,1)^{d-2}/SO(1,1)$ coset models we calculate the conformally exact metric and dilaton, to all orders in the $1/k$ expansion. We consider both vector and axial gauging. We find that these cosets represent two different space--time geometries: ($2d$ black hole)$\otimes \IR^{d-2}$ for the vector gauging and ($3d$ black string)$\otimes \IR^{d-3}$ for the axial one. In particular for $d=3$ and for the axial gauging one obtains the exact metric and dilaton of the charged black string model introduced by Horne and Horowitz. If the value of $k$ is finite we find two curvature singularities which degenerate to one in the semi--classical $k\to \infty$ limit. We also calculate the reflection and transmission coefficients for the scattering of a tachyon wave and using the Bogoliubov transformation we find the Hawking temperature.