Limite Newtoniano em gravitação não-local e correções quânticas

Abstract

In this work, the Newtonian limit of a class of nonlocal models characterized by the form factors fs(□) = exp[(− □ /µ2s)Ns ] is investigated using the effective sources formalism. In the considerations presented here, it is assumed that Ns is a positive real number, not necessarily an integer. As a result, several representations for the effective source, for the mass function, and for the Newtonian potential are obtained, as well as approximations that highlight the dependence of these quantities on the parameters Ns and µs and that can be employed in the phenomenology of the weak-field regime of nonlocal gravity. Furthermore, the reason why Newtonian potential oscillations arise only when Ns > 1 is explained, and it is shown that, despite the presence of such oscillations, the effective mass function is positive for all Ns > 0. It is also verified that the solutions of the linearized equations of motion are regular, that is, they do not exhibit curvature singularities. Finally, logarithmic quantum corrections to the Newtonian potential, to the effective source, and to the mass function are calculated.