On causality and its violation in f(R,Lm,T) gravity

In this paper, $f(R,L_m,T)$ gravity is considered. It is a generalization of the theories $f(R,T)$ and $f(R,L_m)$. This modified theory of gravity exhibits strong geometry-matter coupling. The problem of causality and its violation is verified in this model. Such analysis is carried out using Gödel-type solutions considering different types of matter. It is shown that this model allows both causal and non-causal solutions. These solutions depend directly on the content of matter present in the universe. For the non-causal solution, a critical radius is calculated, beyond which causality is violated. Taking different matter contents, an infinite critical radius emerges that leads to a causal solution. To obtain a causal solution, a natural relationship arises between the parameters of the theory.