electromagnetism - Does Gravity Warp Coulomb's force?

Does gravity effect the "sphericalness" of the Coulomb force?

For example, is the field 1 meter above a charge weaker than the field 1 meter below the charge?

Could a 0.014% difference in the field be detected?

Have there been any such experiments run?

Edit:

In answer to firtree's question below, I am working on the admittedly heretical idea that the "curvature of space" is actually the flow of space into a massive body and as such space is flowing into Earth at 11km/s at its surface (its escape velocity).

At the moment, I'm trying to develop a model for length contraction. Using the notions of perturbation theory and $r=ct$ one could perhaps reformulate Coulomb's Law: $$F(r)=\frac{q_1q_2}{\epsilon_0}\frac{1}{4\pi r^2}$$ as: $$F(t)=\frac{q_1q_2}{\epsilon_0}\frac{1}{4\pi c^2t^2}$$ Time moving against the flow: $$t_u=\frac{d}{c-v}$$ and with the flow: $$t_d=\frac{d}{c+v}$$ The 0.014% comes from comparing the force for the two times plugging in $d=1$ and $v\approx11,000$ m/s

However, as the calculation of length contraction illustrates, the actual effect is dependent on the two way speed of light. And aside from that, if things actually worked this way it would seem to violate Newton's 3rd law. But, I just wanted to get a sanity check and see if there were any experimental (or theoretical) results related to this.