Back reaction of a conformal field on a three-dimensional black hole

The first order corrections to the geometry of the (2+1)-dimensional black hole due to the back reaction of a massless conformal scalar field are computed. The renormalized stress-energy tensor used as the source of Einstein equations is computed using the Green function for the black-hole background with transparent boundary conditions. This tensor has the same functional form as the one found in the nonperturbative case which can be exactly solved. Thus, a static, circularly symmetric, and asymptotically anti--de Sitter black-hole solution of the semiclassical equations is found. The corrections to the thermodynamic quantities are also computed.