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There is, however, a solution to the above problem

The problem with the gravity of gravity arise because of increasing relativistic mass. If a test particle approaches a black hole from infinity and its instantaneous velocity gets very near to light speed then its relativistic mass tends towards infinite. This means that it surpasses the strength of the central mass. In this situation even a single particle could generate a field capable of canceling that of the black hole and effectively move the black hole. If mass were in falling from all directions this should destroy the black hole by negating its field.

I'm afraid it contains gamma and therefore relativistic mass.https://en.m.wikipedia.org/wiki/Four-momentum

: WikiMany contemporary authors such as Taylor and Wheeler avoid using the concept of relativistic mass altogether:"The concept of "relativistic mass" is subject to misunderstanding. That's why we don't use it. First, it applies the name mass - belonging to the magnitude of a 4-vector - to a very different concept, the time component of a 4-vector. Second, it makes increase of energy of an object with velocity or momentum appear to be connected with some change in internal structure of the object. In reality, the increase of energy with velocity originates not in the object but in the geometric properties of spacetime itself."

That is a cop out. Gravity is a force which acts upon mass.

The force of gravity is caused by the length of the second causing a in the g-field at r from M.

And the g-field is caused by M.This being why, despite the equation of F=ma, all value m is accelerated at same rate towards M.