Conservation Laws and 2d Black Holes in Dilaton Gravity

A very general class of Lagrangians which couple scalar fields to gravita-tion and matter in two spacetime dimensions is investigated. It is shown that a vector field exists along whose flow lines the stress-energy tensor is conserved , regardless of whether or not the equations of motion are satisfied or if any Killing vectors exist. Conditions necessary for the existence of Killing vectors are derived. A new set of 2D black hole solutions is obtained for one particular member within this class of Lagrangians. One such solution bears an interesting resemblance to the 2D string-theoretic black hole, yet contains markedly different thermodynamic properties.