An Interpretation of Maxwell Equation by Using the Formalism of Gravitational Waves

摘要

Maxwell equations are known to be fully compatible with the special theory of relativity, but have no representation in terms of space-time perturbations, in opposition with gravitationnal waves which are described as the propagation of small perturbations in the metric of space-time. We propose in this paper to interprete Maxwell equations and electromagnetic waves by using the formalism now well established to describe gravitationnal waves. After deriving a momentum-energy tensor T~(ij) for electromagnetic source, we can apply Einstein's equations in their linearised form. We obtain a wave propagation equation on the metric coefficients which is usually used to explain the propagation of gravitationnal waves. Since this propagation equation is identical as the electromagnetic one, we examine how electromagnetic waves can be interpreted as the propagation of small petrurbations in the space-time metric. We show that in such an interpretation, the electromagnetic potential plays an equivalent role as the gravitationnal potential, and then, can be represented by the metric coefficients. We give the explicite relation between electomagnetic potentials and the metric coefficients which are obtained in this approach and the whole electromagnetic energy associated to a point charge.