Does GR really reduce to Newtonian gravity in low-velocity, weak-field limit?
As we have already noted, Newtonian gravity propagates with unconditionally infinite speed. How, then, can GR reduce to Newtonian gravity in the weak-field, low-velocity limit? The answer is that conservation of angular momentum is implicit in the assumptions on which GR rests. However, as we have already seen, finite propagation speeds and conservation of angular momentum are incompatible. Therefore, GR was forced to claim that gravity is not a force that propagates in any classical sense, and that aberration does not apply. In practice, this suppression of aberration is done through so-called retarded potentials. In electromagnetism, these are called Lienard-Wiechert potentials. For examples of the use of retarded potentials, see (Misner et al., 1973, p. 1080) or (Feynman, 1963, p. 21-4). Suppose we let be the gravitational potential at a field point and time , be the gravitational constant, be an element of volume in the source of the potential, be the coordinates of that volume ele
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