Static and stationary solutions of the Einstein-Maxwell equations

Details Static and stationary solutions of the Einstein-Maxwell equations Static and stationary solutions of the Einstein-Maxwell equations

Jun 1979

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1979gregr..10..681c&link_type=abstract

General Relativity and Gravitation, vol. 10, June 1979, p. 681-697. Research supported by the University of Victoria; National

Mathematics

13

Einstein Equations, Gravitational Fields, Maxwell Equation, Relativity, Charged Particles, Equipotentials, Field Theory (Physics), Laplace Equation, Metric Space, Transformations (Mathematics)

Scientific paper

The Weyl axially symmetric electrovac formalism for coincident gravitational and electrostatic equipotential surfaces is used to generate charged versions of some axially symmetric vacuum fields. The metric for two separated charged Curzon particles held in equilibrium by a strut is found and the condition for the removal of the strut is discussed. Kinnersley transformations applied to the two-particle metric yield spin, but line singularities invariably appear along the symmetry axis and the metric is asymptotically NUT-like. It is shown that any Kinnersley transformation applied to a static axially symmetric asymptotically flat vacuum metric generates another asymptotically flat metric only if the latter is static. Moreover, the transformed metric is always undercharged if it is asymptotically flat. A necessary and sufficient condition for asymptotic flatness in terms of the relevant parameters is found. A generalization of the Kinnersley transformation scheme is presented and illustrated by an example.

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