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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We present a general class of solutions to Einstein's field equations with two spacelike commuting Killing vectors by assuming the separation of variables of the metric components. The solutions can be interpreted as inhomogeneous cosmological models. We show that the singularity structure of the solutions varies depending on the different particular choices of the parameters and metric functions. There exist solutions with a universal big-bang singularity, solutions with timelike singularities in the Weyl tensor only, solutions with singularities in both the Ricci and the Weyl tensors, and also singularity-free solutions. We prove that the singularity-free solutions have a well-defined cylindrical symmetry and that they are generalizations of other singularity-free solutions obtained recently.PACS number(s): 04.20.Jb, 98.80.Dr

The results of our previous paper are applied to solving analytically the balance problem in the double-Kerr solution for all three possible types of binary systems, i.e. when a binary system is composed of two non-extreme black holes, of a non-extreme black hole and a hyperextreme object and of two hyperextreme objects. We also construct a new stationary electrovacuum metric representing binary systems of charged, magnetized, rotating, aligned masses involving one extreme object and on the basis of the numerical study of balance equations we conjecture that the equilibrium states in such systems are impossible.

The general asymptotically flat two-soliton solution of the Einstein-Maxwell equations symmetric about the equatorial plane is considered herein. The complex potentials of this solution and the corresponding metric functions are obtained in the explicit compact form. The balance of two symmetric charged spinning objects is analyzed. 0 1995 American Institute of Physics.