Electromagnetic Fields and Massive Bodies

We consider an example of the effects of massive bodies on static electromagnetic fields in general relativity which yields considerable insight into the fadeaway of multipole moments in nonspherical perturbations of gravitational collapse. We calculate the electromagnetic field of an electrostatic or magnetostatic multipole of fixed strength placed at the center of a massive, nonrotating, spherical shell. If we consider a sequence of static solutions in which the massive shell approaches its own Schwarzschild radius, we find that except in the monopole ($l=0\mathrm{}$) case the value of the multipole moment measured by a distant observer goes to zero. Thus, for an arbitrary (but finite) stationary charge and current distribution inside the shell, in the limit as the shell approaches its Schwarzschild radius the only property of the distribution which can be measured by an external observer is the total electric charge.