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Intuitively, I would not expect gravity to significantly affect electric permitivity. But, Consider a neutral black hole with a plastic sphere outside the event horizon. The protons-electrons of the plastic are polarized with the heavier protons being pulled preferentially closer. A negative charge would be induced on the surface of the sphere. Now, Consider a positively charged relatively mass-less body (positive ion cloud?) surrounded by a plastic sphere. The electrons on the plastic sphere are pulled towards the central charge resulting in a net positive charge measured on the outer surface of the plastic sphere. Measuring the electric field outside the sphere can tell us its permitivity. $E = Q/4*pi*r^2 * permitivity.

Now consider a positively charged black hole with a plastic sphere outside the event horizon. The protons-electrons of the plastic field are affected oppositely by gravity and the central charge. The measured field $E = Q/4*pi*r^2*Permitivity$ would therefore be less outside the plastic sphere.

So for the field to be different outside the plastic sphere , the implication is that the permitivity is different.

is this intuition correct?

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  • $\begingroup$ The equivalence principle prohibits that "protons-electrons of the plastic are polarized with the heavier protons being pulled preferentially closer". $\endgroup$
    – my2cts
    Jan 12 '20 at 20:11
  • $\begingroup$ the equivalence principle posits the equivalence of acceleration due to motion and the acceleration due to gravity. I dont see how that is relevant to the effect of gravity on charge $\endgroup$ Jan 18 '20 at 1:44
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I found the answer:

gravity DOES affect permittivity.

So it seems my2cts comment is un-enlightening and wrong.

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  • $\begingroup$ my2cts comment is correct because you assumed the protons and electrons were treated differently in a gravitational field, which is not true, the change permittivity in the paper is a consequence of time dilation and not a preferential treatment of the particles. $\endgroup$
    – Triatticus
    Jan 25 '20 at 1:41
  • $\begingroup$ They state ‘the permittivity and permeability of free space are modified by the gravity to isotropically decrease of the speed of light’ in order to be consistent with time dilation. That is, time dilation does not ‘cause’ permitivity change as you implied above , rather that time dilation must occur from a fundamental change in the property of space, its permitivity. If protons are so much more massive than electrons, I don’t see why the proton-electron dipole would not align with gravity. Certainly a mathematical treatment would require a quantum theory of gravity which we do not have. $\endgroup$ Jan 26 '20 at 2:24

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