Gödel-type solutions within the f(R, Q, P) gravity

In this work, we scrutinize the consistency of spacetime homogeneous Gödel-type metrics within f ( R , Q , P ) theories of gravity for well-motivated matter sources. As it is well known, such geometries allow for causality violation. We provide general conditions to engender completely causal solutions in a manner completely different from general relativity. We take some specific models, for instance, f(R,Q,P)=R -μ ⁴ⁿ⁺²( a R²+b Q+c P) ⁿ f ( R , Q , P ) = R - μ 4 n + 2 a R 2 + b Q + c P n , to illustrate the general results. Notably, we also find an unusual completely causal vacuum solution in the presence of a non-trivial cosmological constant which corresponds to the case m²=4ω ² m 2 = 4 ω 2 .