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We study the scalar field potential $V(\phi)$ in the scalar-tensor gravitywith self-consistent polytropic stellar configurations. Without choosing aparticular potential, we numerically derive the potential inside variousstellar objects. We restrict the potential to conform to general relativity orto $f(R)$ gravity inside and require the solution to arrive at SdS vacuum atthe surface. The studied objects are required to obtain observationally validmasses and radii corresponding to solar type stars, white dwarfs and neutronstars. We find that the resulting scalar-tensor potential $V(\phi)$ for thenumerically derived polytrope that conforms to general relativity, in eachobject class, is highly dependent on the matter configuration as well as on thevacuum requirement at the boundary. As a result, every stellar configurationarrives at a potential $V(\phi)$ that is not consistent with the other stellarclass potentials. Therefore, a general potential that conforms to all thesepolytropic stellar classes could not be found.

Is scalar-tensor gravity consistent with polytropic stellar models?