Virial theorem in scalar tensor fourth order gravity

Abstract

In this paper, we study, in the Newtonian limit, the virial theorem in the context of a scalar tensor fourth order gravity. In particular, we show, that for a isolated galaxy in viral equilibrium, a specific class of scalar tensor fourth order gravity, i.e. $$f(R,\phi )+\omega (\phi )\,\phi _{;\alpha }\,\phi ^{;\alpha }$$ f ( R , ϕ ) + ω ( ϕ ) ϕ ; α ϕ ; α in not suitable to explain the large fraction of dark matter necessary to have the flatness of the galaxies rotation curves experimentally observed.

Precession shift in curvature based extended theories of gravity and quintessence fields

“…For matter described as a perfect fluid, hence T 00 = ρ and T i j = 0, one gets that, for a ball-like source with radius R, the gravitational potentials { , , A i } and the scalar field ϕ take the form (c = 1) [76,[82][83][84][85]92]…”