2-DIMENSIONAL DILATON GRAVITY COUPLED TO AN ABELIAN GAUGE FIELD

The most general two-dimensional dilaton gravity theory coupled to an Abelian gauge field is considered. It is shown that, up to spacetime d iffeomorphisms and U(1) gauge transformations, the field equations adm it a two-parameter family of distinct, static solutions. For theories with black hole solutions, coordinate-invariant expressions are found for the energy, charge, surface gravity, Hawking temperature, and entr opy of the black holes. The Hawking temperature is proportional to the surface gravity as expected, and both vanish in the case of extremal black holes in the generic theory. A Hamiltonian analysis of the gener al theory is performed, and a complete set of (global) Dirac physical observables is obtained. The theory is then quantized using the Dirac method in the WKB approximation. A connection between the black hole e ntropy and the imaginary part of the WKB phase of the Dirac quantum wa ve functional is found for arbitrary values of the mass and U(1) charg e. The imaginary part of the phase vanishes for extremal black holes a nd for eternal, nonextremal Reissner-Nordstrom black holes.