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

TL;DR

This paper demonstrates that any static, spherically symmetric spacetime can be exactly described as a solution within scalar-tensor gravity theories, with the scalar field potentially changing nature across different regions.

Contribution

It provides a method to represent arbitrary static, spherically symmetric metrics as solutions of scalar-tensor theories with specific coupling functions and potentials.

Findings

Reissner-Nordström metric can be represented in scalar-tensor theory.

Simpson-Visser regularization of Schwarzschild is also representable.

Scalar field can switch from canonical to phantom type across regions.

Abstract

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).