D. Louismartinez et G. Kunstatter, 2-DIMENSIONAL DILATON GRAVITY COUPLED TO AN ABELIAN GAUGE FIELD, Physical review. D. Particles and fields, 52(6), 1995, pp. 3494-3505
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.