Conformally flat noncircular spacetimes

The general metric for conformally flat stationary cyclic symmetric noncircular spacetimes is explicitly derived. In spite of the complexity (due to the noncircular contributions) of the partial differential equations arising from the conformal flatness constraints, they allow for their complete integration in terms of elementary functions. A canonical coordinate representation of the search metric structure is given. Conditions for the existence of a rotation axis (axisymmetry) are established; these conditions coincide with those which restrict the studied noncircular class of spacetimes to be static. As a consequence, a previously known theorem by Collinson is just a part of a more general result: any conformally flat stationary cyclic symmetric spacetime (even a noncircular one) is additionally axisymmetric if and only if it is also static. Recent astrophysical motivations point in the direction of considering stationary noncircular configurations to describe magnetized neutron stars.