ISSN:
1572-9532
Keywords:
MAXWELL EQUATIONS
;
KLEIN-GORDON EQUATION
;
NULL DUST
;
LINEARIZED EQUATIONS
;
EXACT SOLUTIONS
Source:
Springer Online Journal Archives 1860-2000
Topics:
Physics
Notes:
Abstract It is shown that the Maxwell equations with sources, expressed in terms of the covariant tensor field Fijand the current density four-vector Ji, are invariant under the change of the metric gijby gij ′= gij+ liljif liis a principal null direction of Fijand that an analogous result holds in the case of the massless Klein-Gordon equation if liis null and orthogonal to the gradient of the field and in the case of the null dust equations if liis 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 libe a principal null direction of Fij, then (gij+ lilj, Fij) is also an exact solution of the Einstein-Maxwell equations if and only if (lilj, 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.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1023/A:1018802624345
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