It seems difficult to track down a clear explanation of this statement:
So although the Coulomb law was discovered in a supporting frame, general relativity tells us that the field of such a charge is not precisely $1 / r^2$.
Papers I've found seem to say either that the inverse square law for the Coulomb field of a massive point charge remains exactly true in general relativity, or that it has corrections on the order of $1/r^4$ and higher.
I suspect that I may be getting lost in the coordinate transformations and the in-context meaning of $r$. What I would like to know is if general relativity predicts any deviations from the inverse square law for the electric field surrounding a point massive charged particle, as seen by a distant observer.
Presumably the measurement method should be specified, so here's a possibility: Attach a charge $Q$ to an extremely massive particle, then probe the electric field of the charge by first measuring the distribution of electrons, then of positrons, shot at various energies toward the massive particle a la the Rutherford experiment. The difference between the two would be used to subtract out the purely gravitational attraction between the massive particle and the probe particles. I realize that this approach would be impractical for measuring extremely small deviations from Coulomb's law, but it should at least provide a way to dodge some of the difficulties associated with defining $r$ near a point mass. I also realize that quantum corrections would totally change things in real experiment. I'm just looking for a clear classical explanation of what happens to Coulomb's law due to the effects of gravity per general relativity.
EDIT 12/24/18: Specifically: in the scattering measurement proposed above, does it appear to a distant observer that there is a deviation from the inverse square law - a deviation that is a bit different from that due strictly to gravity?