Exact two-soliton solutions to the Einstein gravitational field equations

Details Exact two-soliton solutions to the Einstein gravitational field equations Exact two-soliton solutions to the Einstein gravitational field equations

Oct 1991

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1991ap%26ss.184..313t&link_type=abstract

Astrophysics and Space Science (ISSN 0004-640X), vol. 184, no. 2, Oct. 1991, p. 313-330. Research supported by University and Po

Computer Science

Numerical Analysis

1

Einstein Equations, Gravitational Fields, Solitary Waves, Analytic Functions, Numerical Analysis, Roots Of Equations

Scientific paper

Following previous work on the existence of 1-soliton solution to the Einstein gravitational field equations in the presence of a spherically-symmetric static background field, six sets of analytical 2-soliton solutions to the Einstein field equations were found under a certain ansatz in the absence of the stated background field. Numerical analysis shows that, if the two solitons of the transverse nature are injected at space variable z approaches +/- infinity, the longitudinal field component g33 will acquire nonzero values for a bounded spatial region at later time. The nature of the solitons becomes rather complex when they interact. The amplitude g(micro-nu) of each soliton may change its magnitude resulting from the interaction. It was found that the evolution of one field component might be interpreted as the gravitational instanton in the solutions. The total energy of the interacting solitons remains constant, as expected, at all time. These solutions correspond to the situation where the Riemann tensor is in general nonzero and are truly nontrivial solutions.

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