Cylindrically symmetric spinning Brans-Dicke spacetimes with closed timelike curves

We present here three new solutions of Brans-Dicke theory for a stationary geometry with cylindrical symmetry in the presence of matter in rigid rotation with $T^\mu_\mu\neq 0$. All the solutions have eternal closed timelike curves in some region of the spacetime, the size of which depends on $\omega$. Moreover, two of them do not go over a solution of general relativity in the limit $\omega \to \infty$.