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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.