The authors present in a concise analytical form two asymptotically flat metrics describing the superposition of the Kerr solution with an arbitrary static vacuum Weyl field which differ in their angular momentum distributions. They are then used for the construction of two asymptotically flat generalizations of the Kerr-Newman spacetime possessing the full set of mass-multipole moments able to describe the exterior gravitational field of a charged rotating arbitrary axisymmetric mass.

We demonstrate by the use of Komar integrals that the aggregate mass of two semi-infinite sources which are present in the general family of NUT solutions is a negative nonzero quantity, while the corresponding angular momentum always assumes an infinitely large value except for one particular case when it is equal to zero. In the latter case the solution is equatorially antisymmetric and represents the exterior field of two identical counter-rotating semi-infinite sources possessing negative masses and infinite angular momenta which are attached to the poles of a static Schwarzschild-like finite rod of positive mass.

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A four-parameter class of exact asymptotically flat solutions of the Einstein-Maxwell equations involving only rational functions is presented. It is able to describe the exterior field of a slowly or rapidly rotating neutron star with poloidal magnetic field.