Dinâmica métrico-afim em gravidade modificada – soluções exatas via correspondência RBG-RG.

Abstract

A very pertinent question in Theoretical Physics is the viability of General Relativity (GR) in the high curvature regime, related to several factors such as the presence of unavoidable singularities, with the consequent problem of loss of information and the impossibility of renormalizing the quantized version of theory. On the other hand, in order to agree the theoretical forecast with the results inherent to cosmological and astrophysical observations, GR requires the inclusion of exotic sources (Energy and Dark Matter). The lack of experimental proof of the existence of these exotic components in a direct or indirect way by means other than purely gravitational effects, opens the possibility of considering alternative ways to describe these phenomena. Among them, modifications and extensions of the description of the gravitational interaction. The present work brings a class of Modified Gravity theories, the Ricci-based gravities (RBGs), whose dynamics are described in the metric-affine (or Palatini) formalism. These theories serve as routes of investigation of the mentioned phenomena, avoiding or reducing the need to invoke exotic sources. Within this class of theories, we make a detailed escription of the so-called gravities f(R), EiBI and f(R, RµνRµν). As a work strategy, we built the entire theoretical framework of a Mapping (or Correspondence) method between the RBGs and the GR, applying to the case of matter described by scalar fields. This allows us to treat the quadratic model of gravity f(R) = R + αR2 , in which we apply the presented method, to obtain solutions of this RBG, from a known solution for scalar fields with spherical symmetry in the GR. Finally, we deeply analyze the results obtained, discussing their characteristics and pointing out the compactness of these new objects.