The global Minkowski space c sets the speed limit in physics - not the local speed of light

UPDATE January 27, 2022: We removed our claim that the static electric field would move faster than light in a dielectric medium, like glass. The field presumably can move faster than light in a zone where the polarization capacity of the medium is "saturated". We do not know currently how far this zone extends.

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It is not clear to us what the speed limit of physics is supposed to be in general relativity. How fast does the geometry of spacetime react to changes in the mass distribution?

We have already argued that the local speed of light around a black hole does not set any speed limit for a falling spherical shell. Nor does it restrict the speed of a very large falling mass.

The logical guess is that the universal speed limit of physics is the speed of light in the underlying true geometry of spacetime: the Minkowski space.

https://en.wikipedia.org/wiki/Cherenkov_radiation

An electron which moves faster than the local speed of light in water produces blue Cherenkov radiation. An analogous effect must happen in gravity if a point mass M speeds past the local speed of light.