A cylindrically symmetric solution in Einstein-Maxwell-dilaton gravity

We consider the existence of Einstein-Maxwell-dilaton plus fluid system for the case of stationary cylindrically symmetric spacetimes. An exact inhomogeneous $\epsilon$-order solution is found, where the parameter $\epsilon$ parametrizes the non-minimally coupled electromagnetic field. Some its physical attributes are investigated and a connection with already known G\"odel-type solution is given. It is shown that the found solution also survives in the string-inspired charged gravity framework. We find that a magnetic field has positive influence on the chronology violation unlike the dilaton influence.