Estudos sobre causalidade na gravidade inversa de Ricci

Abstract

This work aimed to find some exact solutions of the field equation of Ricci-Inverse Gravity (RIG). The existence of Closed Timelike Curves (CTCs) is allowed in this model. The field equation of RIG is obtained by adding an anti-curvature term to the EinsteinHilbert action. The FLRW metric has already been studied in the gravity F(R, A), where A is the scalar of the anti-curvature term based on the inverse of the Ricci tensor, i.e., Aµν = R−1 µν . Of the metrics addressed in this work, one brought a pair of solutions, in this case, a term for density and a term for cosmological constant. The solution of the modified equation of RIG obtained here is called an axially symmetric metric, found by Harazika. The density and cosmological constant terms obtained as solutions recover Harazika’s solutions when the coupling (κ) becomes zero, i.e., returning to the unmodified Einstein field equation. Due to the fact that the density allows the coupling constant to be negative or positive, this can alter the energy conditions, specifically the Weak Energy Condition (WEC). Another possibility found consists of including the RIG field equation used in this work in one of the generalized function classes F(R, A) and F(R, AµνAµν), referred to as Class I and Class II, respectively.