Universal conservation law and modified Noether symmetry in 2D models of gravity with matter - art. no. 044001.

It is well known that all 2D models of gravity-including theories with nonv anishing torsion and dilaton theories-can be solved exactly, if matter inte ractions are absent. An absolutely tin space and time) conserved quantity d etermines the global classification of all (classical) solutions. For the s pecial case of spherically reduced Einstein gravity it coincides with the m ass in the Schwarzschild solution. The corresponding Noether symmetry has b een derived previously by Widerin and one of the authors (W.K.) for a speci fic 2D model with nonvanishing torsion. In the present paper this is genera lized to all covariant 2D theories, including interactions with matter. The related Noether-like symmetry differs from the usual one. The parameters f or the symmetry transformation of the geometric part and those of the matte r fields are distinct. The total conservation law (a zero-form current) res ults from a two-stage argument which also involves a consistency condition expressed by the conservation of a one-form matter "current." The black hol e is treated as a special case. [S0556-2821(99)00302-1].