On the physical interpretation of some simple soliton solutions of Einstein's equations

Details On the physical interpretation of some simple soliton solutions of Einstein's equations On the physical interpretation of some simple soliton solutions of Einstein's equations

Nov 1984

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1984gregr..16.1077g&link_type=abstract

General Relativity and Gravitation (ISSN 0001-7701), vol. 16, Nov. 1984, p. 1077-1094.

Physics

13

Einstein Equations, Gravitational Waves, Shock Waves, Solitary Waves, Curvature, Inverse Scattering, Minkowski Space, Shock Fronts, Space-Time Functions

Scientific paper

The simple soliton solutions to Einstein's equations are obtained by Belinski and Zakharov (1978) and are interpreted as gravitational solitary shock waves on the basis of an analysis of the coordinate singularities inherent in inverse scattering. It is shown that the singularities can be removed by an appropriate explicit extension of the solutions. A classification scheme is proposed for the equivalent flat space-time metrics appropriate to the problem, and the matching of the Belinski-Zakharov (B-Z) simple solitons to flat space-time is analyzed in detail. It is found that the problem has more than one solution depending on the type of singularity admitted in the Ricci tensor, and a three parameter solution is obtained which is inequivalent to that of B-Z. It is demonstrated that negative values for the ranges are limited only by curvature singularities. For positive values the coordinate singularities are similar to those of B-Z. It is also found that the matching to flat space-time results in a shock front whose intersection is bounded by any spacelike hypersurface.

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