Vacuum spacetime with closed time-like curves in the context of Ricci-inverse gravity

This research studies primarily centers around a specific vacuum solution of the Einstein’s field equations with a negative cosmological constant, known as a type-D vacuum solution in Anti-de Sitter (AdS) background. The key finding of this study is that the determinant of the Ricci tensor ([Formula: see text]) possesses a nonzero value. This observation ensures that this vacuum spacetime can be investigated within the framework of Ricci-inverse gravity as well. In fact, it has demonstrated that this type-D vacuum solution serves as an exact solution in Ricci inverse gravity in the background of AdS space. Notably, the negative cosmological constant undergoes modification by the coupling constant within this context. Moreover, we show that this gravity theory permits the formation of closed time-like curves at a specific moment in time analogue to the general relativity case. Consequently, this theory introduces an intriguing time-machine model within the domain of Ricci-inverse gravity theory.