Causality and its violation in $f(R,\mathcal{L}_m,\phi,g^{\mu\nu}\nabla_\mu \phi \nabla_\nu \phi)$ gravity

TL;DR

This paper investigates a modified gravity model with a scalar field and matter, analyzing its causal structure through G"{o}del solutions, revealing conditions for causality and the scalar field's role in preventing closed timelike curves.

Contribution

It extends gravity theories by exploring G"{o}del solutions within a complex scalar-matter framework, identifying conditions for causality and the scalar field's influence.

Findings

Standard G"{o}del metric incompatible with scalar sector unless in GR limit.

G"{o}del-type geometries admit solutions with causal or noncausal properties depending on matter.

Scalar field configurations enforce causality, preventing closed timelike curves.

Abstract

A modified gravitational model whose action is given by an arbitrary function of the Ricci scalar, the matter Lagrangian density, a scalar field, and its kinetic term is investigated as an extension of the gravitational sector including an additional dynamical degree of freedom. Within this framework, the causal structure of rotating cosmological solutions is analyzed by considering G\"{o}del and G\"{o}del-type spacetimes as background geometries used as theoretical probes of the model consistency. Different matter sources are examined, including a perfect fluid and scalar-field configurations. It is found that the standard G\"{o}del metric is not compatible with the scalar sector of the theory unless the model reduces to the General Relativity limit. In contrast, G\"{o}del-type geometries admit a wider class of solutions whose causal properties depend on the model parameters and on the matter content. In particular, perfect-fluid sources may lead to either causal or noncausal configurations, whereas scalar-field configurations constrain the geometry to the causal limit, preventing the formation of closed timelike curves, highlighting that the scalar field plays a nontrivial dynamical role distinct from that of a cosmological constant.