Cherenkov radiation

Cherenkov Radiation is a very interesting phenomenom. Recently I asked myself, if such a phenomenom allso exists for gravity in the sense, that if a particle moves faster than the speed of gravity in a medium, it should radiate gravitational cherenkov radiation. I found an article [1], that precisely predicts that. However in there article the theorists use it to constrain vacuum speed of gravity. They do not consider the case that gravity in a medium might(?) have a speed lower than the vacuum speed of gravity.

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