Closed time-like curves in f(R,A) modified gravity theory

In this manuscript, we investigate solutions that allow closed time-like curves (CTCs) in general relativity (GR) within the framework of a modified gravity theory. We consider here an alternative theory recently proposed in gravity theories known as f(R,A)=(R+αA) gravity or Ricci-inverse (RI) gravity, α is the coupling constant. This theory incorporates modifications into the Einstein-Hilbert action through a coupling with an anti-curvature scalar derived from the anti-curvature tensor. We investigate a family of Petrov type-N solutions that are non-vacuum solutions of the field equations, characterized by a negative cosmological constant. The matter-energy content is Vaidya radiation, and its energy density may either remain constant or vary with axial distance. One distinctive feature of the considered solutions is the formation of CTCs, which violate the causality condition. Another observation is that the determinant of the Ricci tensor, Rμν, differs from zero, confirming the existence of an anti-curvature tensor, Aμν, the inverse of the Ricci tensor, defined as Aμν=Rμν−1, and hence, the anti-curvature scalar A=gμνAμν. We demonstrate that the family of cosmological models serves as valid solutions within the framework of Ricci-inverse gravity model, with Vaidya radiation as the matter-energy content whose energy density is modified by the coupling parameter. Thus, our results affirm that the Ricci-inverse gravity theory allows for the existence of CTCs, similar to the case in general relativity.