Model of Dilaton Gravity with Dynamical Boundary: Results and Prospects

We consider a model of two-dimensional dilaton gravity where the strong coupling region is cut off by the dynamical boundary making its causal structure similar to the spherically symmetric sector of the higher dimensional gravity. It is shown that the classical dynamics is fully determined by a single ordinary differential equation which possesses an infinite number of exact solutions. All solutions describe either the solutions describing the full reflection regime at subcritical energies or the black hole formation regime at larger energies. Black hole evaporation effect is taken into account by introduction of a new field mimicking the one-loop conformal anomaly. The semiclassical solutions become nonanalytic and ambiguous. It is proposed to perform analytic continuation of the subcritical solutions describing the full reflection through the complex domain to bypass singularities of real solutions describing collapse. It is supposed that this may lead to the correct saddle point solution saturating the path integral for gravitational scattering amplitude at enough energy for a black hole to form in the classical theory.