An axially symmetric spacetime with causality violation in Ricci-inverse gravity

TL;DR

This paper explores Ricci-inverse gravity, an alternative gravitational theory, demonstrating it permits causality violations through Closed Time-like Curves in axially symmetric spacetimes, and compares these results with general relativity.

Contribution

It introduces Ricci-inverse gravity and shows it allows causality violations, extending known solutions like G"{o}del universes within this new framework.

Findings

Ricci-inverse gravity admits Closed Time-like Curves.

Causality violation relates to matter content.

Comparison with general relativity highlights differences.

Abstract

In this paper, Ricci-inverse gravity is investigated. It is an alternative theory of gravity that introduces into the Einstein-Hilbert action an anti-curvature scalar that is obtained from the anti-curvature tensor which is the inverse of the Ricci tensor. An axially symmetric spacetime with causality violation is studied. Two classes of the model are discussed. Different sources of matter are considered. Then a direct relation between the content of matter and causality violation is shown. Our results confirm that Ricci-inverse gravity allows the existence of Closed Time-like Curves (CTCs) that lead to the violation of causality. Furthermore, a comparison is made between the results of general relativity and Ricci-inverse gravity. Other spacetimes, such as G\"{o}del and G\"{o}del-type universes, which are exact solutions of general relativity and allow for causality violations, are also explored in Ricci-inverse gravity framework.