The Space-Time Metric Outside a Pulsating Charged Sphere

Abstract

We consider the problem of determining the dynamics of the electromagnetic field generated outside a ball whose charge changes depending on time. We are in conditions of perfect symmetry and the electric field is considered to be radial. This is not a simplification since, under such a hypothesis, the magnetic field does not develop. Thus, it is first necessary to find out the appropriate modeling equations. These are obtained by writing a suitable energy tensor that combines the classical electromagnetic stress-energy tensor with a special kind of mass tensor. The next step is to show that it is possible to solve Einstein’s equations by plugging the new tensor on the right-hand side. Interesting connections with some classical solutions related to black holes are finally established.

Newtonian Forces Exerted by Electromagnetic Waves Traveling into Matter

“…Again we get equation (19). The scalar curvature R is not zero and is proportional to p. This can be also checked by taking the trace of ( 14) and recalling that the trace of G αβ is equal to −R and that of U αβ is zero.…”

“…with ρ = div E and c is the speed of light. The above equations were introduced and discussed in [17,18] and further analyzed in [19]. Hence, we refer to those publications for comments and explanations.…”

“…Note that the term ρ V is not necessarily a classical current, but is related to a kind of density charge accompanying the evolution of a wave. The reason for assuming that ρ can attain values different from zero also in vacuum is explained for instance in [19].…”

“…We can say something regarding a charged dielectric sphere. The preparatory work was done in the recent paper [19].…”

“…We are in the spherical system of coordinates (ct, r, θ, φ). As in [19], we look for a metric of the form:…”