G\"{o}del-type universes in Palatini f(R) gravity

TL;DR

This paper investigates whether Palatini f(R) gravity theories allow G"odel-type solutions with closed time-like curves, finding that certain models can avoid causality violations present in general relativity, especially with scalar field matter.

Contribution

It extends G"odel-type solution theorems to Palatini f(R) gravity and shows these theories can prevent causality violations under specific conditions.

Findings

Palatini f(R) gravity admits G"odel-type solutions with causal structure.

Certain f(R) models constrained by observational data do not admit G"odel geometry.

Scalar field matter leads to G"odel solutions without causality violation.

Abstract

We examine the question as to whether the Palatini f(R) gravity theories permit space-times in which the causality is violated. We show that every perfect-fluid G\"{o}del-type solution of Palatini f(R) gravity with density $\rho$ and pressure $p$ that satisfy the weak energy condition $\rho+p \geq 0$ is necessarily isometric to the G\"odel geometry, demonstrating therefore that these theories present causal anomalies in the form of closed time-like curves. This result extends a theorem on G\"{o}del-type models to the framework of Palatini f(R) gravity theory. We concretely examine the G\"odel-type perfect-fluid solutions in specific $f(R) = R - \alpha/R^{n}$ Palatini gravity theory, where the free parameters $\alpha$ and $n$ have been recently constrained by a diverse set of observational data. We show that for positive matter density and for $\alpha$ and $n$ within the interval permitted by the observational data, this theory does not admit the G\"odel geometry as a perfect-fluid solution of its field equations. In this sense, this theory remedies the causal pathology in the form of closed time-like curves which is allowed in general relativity. We derive an expression for a critical radius $r_c$ (beyond which the causality is violated) for an arbitrary Palatini f(R) theory, thus making apparent that the violation of causality depends on the form of f(R) and on the matter content components. We also examine the violation of causality of G\"odel-type by considering a single scalar field as the matter content. For this source we show that Palatini f(R) gravity gives rise to a unique G\"odel-type solution with no violation of causality.