The double-Kerr solution

The exact double-Kerr solution of Kramer and Neugebauer is analysed by expanding it in powers of the masses m1, m2. For general values of the parameters the solution contains NUT sources and therefore is not flat at spatial infinity. These do not occur (or can be removed) in two special cases: (I) if a1/m1 = a2/m2, where a1, a2 are the angular momenta per unit mass; (II) if a1 + a2 = 0. In case (I) there is present, in addition to the two spinning objects, a massless spinning rod of finite length. The spacetime in this case contains closed timelike curves (CTC) even though the sources are realistic and lie in a compact region. We conclude that, in the absence of an explanation of CTC, general relativity does not give a satisfactory account of this physical system