It is known that Maxwell's equations can be derived from Coulomb's Law and Special Relativity. Since Coulomb's Law is so similar to Newton's law of universal gravitation, is it also possible to derive Maxwell-like equations from Newton's law of universal gravitation and special relativity?

I suspect the answer is no, because I've never seen it done and I am guessing that the fact that charge can be positive or negative while mass can only be positive has something to do with why not.

  • $\begingroup$ I think some of the components of the stress-energy tensor becomes newtons law of gravitation (in the potential form) in some kind of limit. If I remember correct it is the components with the time coordinate (0). Since Maxwells equations do not have mass in them as far as I remember it seems unlikely. $\endgroup$
    – Emil
    Apr 6, 2017 at 19:55
  • $\begingroup$ Hint: Look up gravitoelectromagnetism. $\endgroup$
    – Qmechanic
    Apr 6, 2017 at 21:01
  • $\begingroup$ It has been tried, and you get "similar" equations to Maxwell's. One of the problems is that it does not bend light. Another is negative energy waves, although this last one I am not sure why is a problem (page 81 of MTW). $\endgroup$
    – user126422
    Apr 6, 2017 at 23:21
  • $\begingroup$ This one does show the steps and some references, although I am not sure if it is correct.vixra.org/abs/1701.0533 $\endgroup$
    – user126422
    Apr 6, 2017 at 23:25


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