G\"{o}del-type solutions in $f(R,T,R_{\mu\nu} T^{\mu\nu}$) gravity

TL;DR

This paper investigates G"odel-type solutions within a modified gravity model that couples curvature and matter, revealing conditions for both causal and non-causal universes depending on matter content.

Contribution

It demonstrates that $f(R,T,R_{ ueta} T^{ ueta})$ gravity admits both causal and non-causal G"odel-type solutions, highlighting the influence of matter content on causality.

Findings

Existence of both causal and non-causal solutions in the model

Critical radius for causality violation depends on matter content

Infinite critical radius leads to causal solutions with parameter relationships

Abstract

In this paper, $f(R,T,R_{\mu\nu} T^{\mu\nu}$) gravity is considered. It is a modified theory of gravity that exhibits a strong coupling of gravitational and matter fields. Therefore, if gravity is governed by this model a number of issues must be re-examined. In this context, the question of causality and its violation is studied. Such analysis is carried out using the G\"{o}del-type solutions. It is shown that this model allows both causal and non-causal solutions. These solutions depend directly on the content of matter present in the universe. For the non-causal solution, a critical radius is calculated, beyond which causality is violated. Taking different matter contents, an infinite critical radius emerges that leads to a causal solution. In this causal solution, a natural relationship emerges between the parameters that determine the matter considered.