  Within the generalized Newton-Cartan theory, Galilean Twisted spacetimes are
introduced as dual models of the well-known relativistic twisted spacetimes. As
a natural generalization, torqued vector fields in Galilean spacetimes are
defined, showing that the local structure of a Galilean spacetime admitting a
timelike torqued vector field is given by a Twisted spacetime. In addition,
several results assuring the global splitting as Twisted spacetime are
obtained. On the other hand, completeness of free falling observers is studied,
as well as general geodesic completeness.
