On the time-evolution of the Robinson-Trautman solutions

Details On the time-evolution of the Robinson-Trautman solutions On the time-evolution of the Robinson-Trautman solutions

Jan 1985

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1985cqgra...2...77v&link_type=abstract

Classical and Quantum Gravity (ISSN 0264-9381), vol. 2, Jan. 1, 1985, p. 77-86. Research supported by the Fonds National de la R

Mathematics

8

Bodies Of Revolution, Einstein Equations, Gravitation Theory, Relativity, Singularity (Mathematics), Space-Time Functions, Astronomical Models, Ellipsoids, Power Series, Rotating Spheres, Series Expansion

Scientific paper

The time evolution of the solutions of Robinson and Trautman (1962) for the Einstein field equations of an initial surface of revolution only slightly perturbed from a sphere is investigated analytically, using a power-expansion algorithm in the linear approximation to demonstrate that singularity-free solutions exist for this class of Robinson-Trautman metrics and that the line elements describe the gravitational field of perfectly regular radiating bounded sources. The case of an ellipsoid of revolution is examined explicitly, and the shape of the ellipsoid is found to be preserved in the time evolution.

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