Godel Universe in $f(Q,T)$ gravity: Exploring causality violation and closed time-like curves

In this work, the classical Godel solution from general relativity is extended into the framework of modified gravity theories based on non-metricity $Q$ and the trace of the energy-momentum tensor $T$ in the context of $f(Q,T)$ gravity. The main feature of the Godel solution is the existence of closed time-like curves, which allow for causality violation and time travel. Since general relativity and its extensions do not demand spacetime to be globally causal, there is good motivation to explore such solutions. We have found classes of solutions with different matter content, like perfect fluid, cosmological constant, massless scalar field, etc. It is observed that, for suitable initial conditions, there is always a possibility of obtaining feasible solutions that violate causality in our setup. The presence of non-metricity in such solutions produces crucial deviations that are noteworthy.