Regular black holes and boson stars in semiclassical gravity

We use a Hamiltonian version of the semiclassical Einstein equation to study classical gravity coupled to a quantum scalar field with potential in spherical symmetry. The system is defined by effective constraints where the matter terms are replaced by their expectation values in a quantum state. For the static case, we find numerically that the resulting equations admit asymptotically flat, de Sitter, and anti-de Sitter boson star and regular black hole solutions. We also show that the Bardeen and Hayward nonsingular black hole proposals (and some generalizations thereof) are not solutions to our equations.