Arbitrary static, spherically symmetric space-times as solutions of scalar-tensor gravity

Understand

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).