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