Linearization procedure for cylindrically and axially symmetric space-times

Details Linearization procedure for cylindrically and axially symmetric space-times Linearization procedure for cylindrically and axially symmetric space-times

May 1982

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1982gregr..14..429b&link_type=abstract

General Relativity and Gravitation, Volume 14, Issue 5, pp.429-438

Computer Science

1

Scientific paper

An investigation of the vacuum Einstein gravitational field equations for cylindrically and axially symmetric space-times is presented which leads to an equivalent differential system involving a simple nonlinearity only. The case when this equivalent system is linear is analyzed in detail and two methods for generating solutions of the Einstein vacuum equations are set up. As a result, in the axially symmetric case the linearity of the equivalent system characterizes completely the Kramer-Neugebauer transforms of Papapetrou line elements. Accordingly, Weyl solutions are shown to generate exhaustively both Lewis and van Stockum solutions. Analogous results are obtained also in the cylindrically symmetric case.

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