On solving Einstein's field equations in the Newman-Penrose formalism.

Details On solving Einstein's field equations in the Newman-Penrose formalism. On solving Einstein's field equations in the Newman-Penrose formalism.

Sep 1985

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1985gregr..17..815l&link_type=abstract

General Relativity and Gravitation, Volume 17, Issue 9, pp.815-829

Physics

1

General Relativity

Scientific paper

Using the Newman-Penrose formalism and Penrose's conformai rescaling a method is presented for finding systematically solutions of (or, at least, reduced equations for) the general field equations. These solutions are necessarily (locally) asymptotically flat and are represented in a coordinate system based on a geodesic, twist-free, expanding null congruence. All redundant equations are disposed of and the freely specifiable data are clearly exhibited. Although the few equations that remain to be solved are, in general, intractable, well-known theorems guarantee the existence and uniqueness of solutions. The method applies to ? spaces and ? ? spaces as well as to real space-times.

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