An electric field does polarize the space around a gravitating object - in the global view

In this blog we have several times mentioned that the electric force seems to be weaker in a low gravitational potential - from the point of view of an observer far away.

When a local observer measures the field, he may get a result that moving a 1 coulomb test charge for 1 meter horizontally consumes 1 joule of his energy. But when he transmits that 1 joule as light to the distant observer, there is a redshift, and the distant observer measures the energy less than 1 joule.

For a static electric field, there should exist a static global potential function to ensure the conservation of energy. The natural way is to define that potential as the energy which the distant observer must use to move a test charge to a specific location in space.

If we define the electric field as the gradient of that global potential, we get the electric field from the distant observer's perspective, and he sees less lines of force than a local observer in a low gravitational potential. Thus, the global observer sees that Gauss's law does not hold in a gravitational field. This assumes that the local observers see Gauss's law holding in their local measurements.

The global observer may interpret this that the electric field has electrically polarized space in a low gravitational potential. Now we see the analogy to an optically dense medium. An electric field causes polarization in the charges of the medium. We may interpret the gravitational lensing effect in the same way as how ordinary lenses work: the speed of light is slowed down by polarizable charges in the medium.