https://www.sciencedirect.com/science/article/pii/0003491657900490
Charles Misner and John Wheeler tried to combine Maxwell's equations and a curved spacetime. Their 1957 paper Classical physics as geometry is reprinted in Wheeler's 1962 book Geometrodynamics.
Let us find out how they handled a static electric field under a gravitational field.
The authors suggest that a static charge is really lines of force oozing out of a very small wormhole. They state that lines of force never end and Gauss's law holds.
But how do they treat the case where an electron falls through a big wormhole to a white hole?
A low gravitational potential causes charge polarization?
The refractive index of a medium is
sqrt(relative permittivity
× relative permeability).
There is polarization of charges in the medium under an electric field.
What about a low gravitational potential? On light it acts like a medium of a high refractive index. Is there polarization of charges?
If there is polarization, then Gauss's law does not hold.
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