ISSN:
1089-7658
Source:
AIP Digital Archive
Topics:
Mathematics
,
Physics
Notes:
The possibility of assigning topological properties to gravisolitons has been recently discussed by Belinsky, who considered perturbations of certain diagonal metrics with two commuting Killing vectors. The discussion given by Belinsky relies on the properties of the solitonic part of the projection of the four-dimensional space–time metric onto the two-dimensional space spanned by the Killing vectors. In that context, for single soliton perturbations, he finds two types of, in principle, disjoint solutions, characterized respectively by the functions μin and μout, 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-dimensional metric, it is possible to construct locally smooth extensions that connect sectors associated to μin to sectors associated to μout. Therefore, the concept of "topological charge'' for this type of gravisolitons needs to be revised. Some ideas in this direction are discussed in this paper. We also show that this behavior is not restricted to the particular case of a Bianchi-type VI0 background, but holds in general for the whole set of diagonal background metrics considered by Belinsky. An interesting side result is that the soliton perturbation "erases'' the "cosmological'' singularity that appears naturally in the background metrics, and that they can be extended to regions not covered in the original charts. In the particular case of a Bianchi-type VI0 background, the resulting extended metric is regular everywhere. Finally we present an extension of the soliton metric to the background by matching these metrics through a null hypersurface. This extension requires the presence of a "null dust'' on the matching hypersurface, and therefore the resulting space–time is not a vacuum everywhere. © 1996 American Institute of Physics.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1063/1.531732
Permalink
