Keywords

Einstein-Maxwell equation, new solutions, Killing vector

Abstract

Methods are discussed with which one may derive theorems which allow one to generate new solutions of the Einstein-Maxwell equations from old ones. The old solutions used to generate new ones must admit at least one nonnull Killing vector and may be required to satisfy other conditions, depending on the theorem derived. Examples of derivable theorems are shown; these theorems are used in turn to show how generation of new solutions is accomplished. Examples of the latter are shown, such as generation of Brill or electrified NUT space from the Schwarzschild solution, generation of a new twisted Melvin universe from flat space, and generation of a new generalization of the Ozsvath-Schcking metric. Possible physical interpretations, uses, and extensions of this type of theorem are discussed.

Original Publication Citation

Harrison, Kent B."New Solutions of the Einstein-Maxwell Equations from Old." Journal of Mathematical Physics 9 (1968): 1744-1752.