Has any in-the-lab experiment confirmed the validity of the Reissner-Nordstrom metric for a charged, spherically, symmetric mass.

Question

In 'Solutions to the (RN), Kerr, & Kerr-Newman problems in 4th order conformal, Weyl gravity', P. Mannheim writes, "We find that, unlike the familiar 2nd order Einstein case where the modification to the Schwarzschild metric is in the form of a term which behaves like 1/r^2, in the 4th order case the modification is found to behave like 1/r, i.e. just like the Newtonian potential term itself."  So the crystalized question is, - Is it 1/r or 1/r^2?  Mainstream's treatment of the validity of RN metric, predominantly, involve celestial bodies and their orbits whose tight fit on the possessed charge of the involved is questionable. The enormous consequences of 1/r vs 1/r^2 drives this discussion.  Forgive the crudeness of the following, to make a point. In a sort of modified Rebeka-Pound (RP) experiment, directing a laser of known frequency through the center of a ring of electrical, charge (I believe this is called photorefraction modulation), would change the frequency (among other factors), the question is how much - who would get the nod Einstein or Mannheim?   2nd Question: How would one make the basic calculation of the change of frequency after the beam passes through the ring of charge?    Another concern is the feebleness of the modification as the laser frequency as it passes through the loop - could it be measured?  A thought on that concern, involves comparing the tower RP experiment with a beam passing through the charged ring and repeating it but removing the charged ring. It is the astonishing sensitivity of modern interferometers which discourages the abandonment of the whole idea and of course the size of the equipment (I believe an atom interferometer would require a lab the size of Madison Square Garden.  Any comments, insights, corrections, etc. would be most appreciated.  Thank you for your time.                The Best, Joe Poveromo