TOPOLOGICAL PROPERTIES OF SINGLE GRAVISOLITONS

The possibility of assigning topological properties to gravisolitons h as been recently discussed by Belinsky, who considered perturbations o f certain diagonal metrics with two commuting Killing vectors. The dis cussion given by Belinsky relies on the properties of the solitonic pa rt of the projection of the four-dimensional space-time metric onto th e two-dimensional space spanned by the Killing vectors. In that contex t, for single soliton perturbations, he finds two types of, in princip le, disjoint solutions, characterized respectively by the functions mu (in) and mu(out), such that one can assign a ''topological charge'' to the corresponding space-time. In this article we analyze this problem , studying in detail the single soliton perturbation of a Bianchi-type VI0 background, and prove that when we consider the full four-dimensi onal metric, it is possible to construct locally smooth extensions tha t connect sectors associated to mu(in) to sectors associated lo mu(out ). Therefore, the concept of ''topological charge'' for this type of g ravisolitons needs to be revised. Some ideas in this direction are dis cussed in this paper. We also show that this behavior is not restricte d to the particular case of a Bianchi-type VI0 background, but holds i n general for the whole set of diagonal background metrics considered by Belinsky. An interesting side result is that the soliton perturbati on ''erases'' the ''cosmological'' singularity that appears naturally in the background metrics, and that they can be extended to regions no t covered in the original charts. In the particular case of a Bianchi- type VI0 background, the resulting extended metric is regular everywhe re. Finally we present an extension of the soliton metric to the backg round by matching these metrics through a null hypersurface. This exte nsion requires the presence of a ''null dust'' on the matching hypersu rface, and therefore the resulting space-time is not a vacuum everywhe re. (C) 1996 American Institute of Physics.