| Summary: | Abstract 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, $$f(R,Q,P)=R -\dfrac{\mu ^{4n+2}}{\left( a R^2+b Q+c P\right) ^n}$$ 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 $$m^2=4\omega ^2$$ m 2 = 4 ω 2 .
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