Boulware state in exactly solvable models of 2D dilaton gravity

We discuss self-consistent geometries and behavior of dilaton in exactly solvable models of 2D dilaton gravity, with quantum fields in the Boulware state. If the coupling H(φ) between curvature and dilaton φ is non-monotonic, backreaction can remove the classical singularity. As a result, an everywhere regular star-like configuration may appear, in which case the Boulware state, contrary to expectations, smooths out the system. For monotonic H(φ) exact solutions confirm the features found before with the help of numerical methods: the appearance of the bouncing point and the presence of isotropic singularity at the classically forbidden branch of the dilaton.