Selection criteria for two-parameter solutions to scalar-tensor gravity

We investigate the generic properties of static, spherically symmetric, asymptotically flat solutions to the field equations describing gravity minimally coupled to a nonlinear self-gravitating real scalar field. Five corollaries and a theorem on selection criteria for two- and one-parametric solutions are proven and conditions for obtaining particle-like solutions, black holes or naked singularities are derived. A series of exact solutions in closed forms including different black holes, naked singularities and particle-like solutions, all of which obey the weak energy condition at spatial infinity, are provided. Two further corollaries elaborate on the behavior of solutions at spatial infinity, critical mass, mass density, pressure and energy conditions.