Causality Violating Solutions in Curvature-Squared Gravity

TL;DR

This paper investigates causality violations in curvature-squared gravity, analyzing G"odel-type solutions for closed timelike curves and the role of the Weyl tensor in these models.

Contribution

It demonstrates that G"odel and G"odel-type metrics are causal solutions in this gravity model, and explores the Weyl tensor's influence on energy conditions.

Findings

G"odel solutions are causal in curvature-squared gravity, allowing CTCs.

Weyl tensor contributions are absent in certain solutions, but affect energy density in others.

Modifications to the weak energy condition are observed when considering the Weyl tensor.

Abstract

In this paper, we consider some causality violating solutions in the curvature-squared gravity in order to examine whether closed timelike curves (CTCs) are allowed in these models. These aspects are studied in terms of the G\"odel, G\"odel-type and axially symmetric cosmological solutions. We observe that the G\"odel and G\"odel-type metrics are causal solutions of the model so that CTCs are now allowed and, surprisingly, every contribution involving the Weyl tensor is removed from the solutions. Hence, in order to study the effect (if any) of the Weyl tensor (an conformal symmetry) into CTCs a third metric is considered. In this case, we obtain contributions due to the Weyl tensor to the energy density and led to modifications of the weak energy condition.