Arbitrary Static, Spherically Symmetric Space-Times as Solutions of Scalar-Tensor Gravity

It is shown that an arbitrary static, spherically symmetric metric can be presented as exact solution of a scalar-tensor theory (STT) gravity with certain nonminimal coupling function $f(\phi)$ and potential $U(\phi)$. The scalar field in this representation change its nature from canonical to phantom on coordinate spheres. This representation, however, valid general not the full range radial but only piecewise. Two examples STT representations are discussed: for Reissner-Nordstr\"om Simpson-Visser regularization Schwarzschild (the so-called black bounce space-time).