Cosmological constant Petrov type-N space-time in Ricci-inverse gravity

Abstract: Our focus is on a specific type-N space-time that exhibits closed time-like curves in general relativity theory within the framework of Ricci-inverse gravity model. The matter-energy content is solely composed of a pure radiation field, and it adheres to the energy conditions while featuring a negative cosmological constant. One of the key findings in this investigation is the non-zero determinant of the Ricci tensor ($R_{\mu\nu}$), which implies the existence of an anti-curvature tensor ($A^{\mu\nu}$) and, as a consequence, an anti-curvature scalar ($A \neq R^{-1}$). Furthermore, we establish that this type-N space-time serves as a solution within modified gravity theories via the Ricci-inverse model, which involves adjustments to the cosmological constant ($\Lambda$) and the energy density ($\rho$) of the radiation field expressed in terms of a coupling constant. As a result, our findings suggest that causality violations remain possible within the framework of this Ricci-inverse gravity model, alongside the predictions of general relativity.