Gödel and Gödel-type solutions in the Palatini f(R,T) gravity theory

Abstract

The Palatini [Formula: see text] gravity theory is considered. The standard Einstein–Hilbert action is replaced by an arbitrary function of the Ricci scalar [Formula: see text] and of the trace [Formula: see text] of the energy-momentum tensor. In the Palatini approach, the Ricci scalar is a function of the metric and the connection. These two quantities, metric and connection, are taken as independent variables. Then, it is examined whether Palatini [Formula: see text] gravity theory allows solutions in which lead to violation of causality. The Gödel and Gödel-type spacetimes are considered. In addition, a critical radius, which permits to examine limits for violation of causality, is calculated. It is shown that, for different matter contents, noncausal solutions can be avoided in this Palatini gravitational theory.

Gödel-type solutions in $$f(R,T,R_{\mu \nu } T^{\mu \nu }$$) gravity

“…Causality is also discussed in Chern-Simons gravity [30,31], f (T ) gravity [32], f (R, T ) gravity [33], bumblebee gravity [34], Horava-Lifshitz gravity [35], Brans-Dicke theory [36] and f (R, Q) gravity [37]. More recently causality is discuss in f (R, φ, X ) and f (R, T ) Palatini gravity [38,39]. In this paper, the main objective is to investigate whether the f (R, T, R μν T μν ) gravity allows for causality violation.…”

Gödel-type solutions in hybrid metric-Palatini gravity

“…These CTCs appear in other cosmological models that have hyperbolic or spherical symmetry, such as Kerr black hole, Van-Stockum model, cosmic string, among others [26,27]. The causality problem has been verified in many gravitational theories, such as, f (R) theory [28], k-essence theory [29], Chern-Simons gravity [30,31], f (T ) gravity [32], f (R, T ) gravity [33], bumblebee gravity [34], Horava-Lifshitz gravity [35], Brans-Dicke theory [36], f (R, Q) gravity [37], f (R, φ, X) gravity [38], f (R, T ) Palatini gravity [39], among others.…”