On the geometric structure of nonstationary multisoliton vacuum metrics with real pole trajectories on a general background

Abstract

We present an analysis of the geometric structure of nonstationary multisoliton vacuum metrics obtained from a general background using the inverse scattering method of Belinsky and Zakharov. In the case of real pole trajectories, in general the algorithm leads, for ann-soliton metric, ton+1 disjoint coordinate patches. We show, by an explicit construction, that each coordinate patch can be smoothly extended to a separate spacetime manifold. As a result we find that there are no shock fronts associated with the pole trajectories and that, contrasting with the situation for pairs of complex pole, there are no structures that can be easily identified with the region of interaction of a given number of solitons.