Izvestiya of Saratov University.

Physics

ISSN 1817-3020 (Print)
ISSN 2542-193X (Online)


For citation:

Zayko Y. N. An Explicit Solutions of the Maxwell-Einstein Equations. Izvestiya of Sarat. Univ. Physics. , 2010, vol. 10, iss. 1, pp. 50-58. DOI: 10.18500/1817-3020-2010-10-1-50-58

This is an open access article distributed under the terms of Creative Commons Attribution 4.0 International License (CC-BY 4.0).
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Russian
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UDC: 
537.8; 539.186.2

An Explicit Solutions of the Maxwell-Einstein Equations

Autors: 
Zayko Yuri Nikolaevich, Stolypin’s Volga Regional Academy of State Service
Abstract: 

This article concerns the effect of gravitation field of the spherical electro-magnetic wave (EMW) on its propagation in vacuum. For this it was received a solution of the coupled Maxwell-Einstein equations. The expression for metric is supposed to be just the same as in wellknown Schwarzschild problem for gravitation field at the vicinity of point mass with additional dependence on polar angle 9. The equations for radial and angular parts of EMW fields of ТЕ- and TM-types are received. Their various solutions are Investigated. It is shown that in addition with traveling wave EMW at a great distance some new solution of so-called instanton type exists. It describes the process of quantum tunneling between degenerate states corresponding to convergent and divergent spherical waves in quasiclassical approximation. An explicit solutions for waves of both types are received so as an expressions for corresponding metrics. The solutions of the Maxwell-Einstein (Maxwell) equations are considered for waves which have zero value of moment momentum. It was shown that in static case they describe fields of point charges - electric e and magnetic m. It was shown that symmetry of Maxwell equations with respect to group L/(1) of dual transformations: (E+/H)-> (E+iH)'", E and H are electric and magnetic fields, a - is real parameter is valid for generalized charge e + im, which is transformed in the same manner. Spontaneous breaking of symmetry of this group, which is characterized tga = -m/e, leads to arising massless particles - photons due to Goldstone theorem. This also leads to the fact that magnetic charges cannot detect in Nature.

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