By Einstein's Equivalence Principle that is an acceleration. I call it an Unmoving Acceleration that through gravity produces weight in matter. Since it is unmoving it has no rate. So the rate must be taken out of the Equivalence Principle for the sake of gravity. There is always rate for an accelerating frame and that is unlimited.
When you take the rate out for gravity it becomes limited. There is a maximum weight for anything in gravity and that is not approaching infinity but instead light speed. This effects the astrophysics of the pressure inside stars. It is limited weight.
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