Black holes in two dimensional space-times are toy models to understand the physics of their four dimensional analogs. Since the general theory of relativity has no physical contents in two dimensions (Collas (1977)), other 2-D gravity theories have been considered, in particular string theory for which there is two dimensional black hole solutions (Callan et al. (1992)). It is possible, however, to extract from the equations of general relativity a gravity theory by considering the formal limit , where is the dimension of space-time (Mann (1992), Mann & Ross (1993)). One obtains the equation
where , is Newton's constant and where is the trace of the classical energy-momentum tensor . This equation is supplemented by the continuity equation
which follows also from the equations of general relativity.