Physics
Scientific paper
Mar 1998
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1998gregr..30..379t&link_type=abstract
General Relativity and Gravitation, Volume 30, Issue 3, p.379-387
Physics
4
Scientific paper
It is shown that the Maxwell equations with sources, expressed in terms of the covariant tensor field $Fij$ and the current density four-vector $Ji$, are invariant under the change of the metric $gij$ by $g'ij = gij + li lj$ if $li$ is a principal null direction of $Fij$ and that an analogous result holds in the case of the massless Klein-Gordon equation if $li$ is null and orthogonal to the gradient of the field and in the case of the null dust equations if $li$ is parallel to the dust four-velocity. An elementary proof of the following generalization of the Xanthopoulos theorem is also given: Let $(gij, Fij)$ be an exact solution of the Einstein-Maxwell equations and let $li$ be a principal null direction of $Fij$, then $(gij + li lj, Fij)$ is also an exact solution of the Einstein-Maxwell equations if and only if $(li lj, 0)$ satisfies the Einstein-Maxwell equations linearized about the background solution $(gij, Fij)$. Furthermore, analogous theorems, where the source of the gravitational field is a massless Klein-Gordon field or null dust, are presented.
Mondragón-Sánchez J. A.
Torres Del Castillo G. F.
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