QUANTUM FLUCTUATIONS AND CURVATURE SINGULARITIES IN JACKIW-TEITELBOIMGRAVITY

Jackiw-Teitelboim gravity with matter degrees of freedom is considered . The classical model is exactly solvable and its solutions describe n ontrivial gravitational scattering of matter wave packets. For a huge amount of the solutions the scattering space-times are free of curvatu re singularities. However, the quantum corrections to the field equati ons inevitably cause the formation of curvature singularities, vanishi ng only in the limit HBAR --> 0. The singularities cut the space-time and disallow propagation to the future. The model is inspired by the d imensional reduction of 4D pure Einstein gravity, restricted to space- times with two commuting spacelike Killing vectors. The matter degrees of freedom also stem from the 4D ansatz. The measures for the continu al integrations are judiciously chosen and one-loop contributions (inc luding the graviton and the dilaton ones) are evaluated. For the numbe r of the matter fields N = 24 we obtain even the exact effective actio n, applying the David-Distler-Kawai procedure. The effective action is nonlocal, but the semiclassical equations can be solved by using some theory of the Hankel transformations.