G\"odel solution in the bumblebee gravity
  Here, we consider a gravity theory involving a spontaneous Lorentz symmetry breaking called the bumblebee model. We show that, at certain values of the bumblebee field, the G\"odel metric is consistent within this theory. 
J. R. Nascimento, A. Yu. Petrov, A. F. Santos and W. D. R. Jesus
hep-th