The Asymptotic Structure of Algebraically Special Space – times

It is shown that the only vacuum algebraically special space-time that is asymptotically simple is Minkowski space. The structure of null infinity for algebraically special space-times satisfying a subset of the vacuum equations is shown to be particularly simple in terms of the coordinates used in Kerr's original reduction of the field equations. With the assumption of the existence of a global future null infinity, I + , (in the sense of having topology S 2 × R), past null infinity can be constructed with the same topology and canonically identified with future null infinity. This identifies the corresponding asymp-totic data. The Bondi momentum on corresponding cuts of future null infinity and past null infinity sum to zero. In particular the Bondi energy is negative or zero on one of future or past null infinity thus implying singularities or negative energy densities in the interior if the space-time is nontrivial. In the first appendix the shear and radiation fields at null infinity are all derived. In a second appendix the Cauchy Riemann structure on the space of geodesics of the congruence underlying these space-times is considered and the auxilliary structures required to determine the spacetime are characterised intrinsically with respect to the Cauchy Riemann structure.