11521 10.1140/epjc/s10052-023-11521-y 331 65 Gödel-type solutions within the f(R, Q, P) gravity Regular Article - Theoretical Physics 1 9 2023 4 17 2023 3 2 2023 4 17 2023 4 26 Conselho Nacional de Desenvolvimento Científico e Tecnológico 301562/2019- 9 The Author(s) 2023 Open AccessThis article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/ . Funded by SCOAP3. SCOAP3 supports the goals of the International Year of Basic Sciences for Sustainable Development. 10052 83 83 4 4 J. R. Nascimento jroberto@fisica.ufpb.br A. Yu. Petrov petrov@fisica.ufpb.br P. J. Porfírio pporfirio@fisica.ufpb.br Ramires N. da Silva rns2@academico.ufpb.br grid.411216.1 0000 0004 0397 5145 Departamento de Física Universidade Federal da Paraíba Caixa Postal 5008 João Pessoa Paraíba 58051-970 Brazil 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 - 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 ω 2 .