  Using the quasi-Maxwell formalism, we derive the necessary and sufficient
conditions for the matching of two stationary spacetimes along a stationary
timelike hypersurface, expressed in terms of the gravitational and
gravitomagnetic fields and the 2-dimensional matching surface on the space
manifold. We prove existence and uniqueness results to the matching problem for
stationary perfect fluid spacetimes with spherical, planar, hyperbolic and
cylindrical symmetry. Finally, we find an explicit interior for the cylindrical
analogue of the NUT spacetime.
