GR and Newton give almost exactly the same result for the orbits of planets and the acceleration of falling bodies. Is it an incredible coincidence, or does GR have some tiny term (e.g., ict) that accounts for the difference? Is it possible to make GR collapse to Newton's law by ignoring that tiny term?

  • $\begingroup$ Possible duplicates: physics.stackexchange.com/q/211930/2451 and links therein. $\endgroup$ – Qmechanic Oct 16 '20 at 5:08
  • $\begingroup$ Yes, it is! The effective potential in the Schwartzschild solution is equal to that in Newtonian gravitation (en.wikipedia.org/wiki/Effective_potential) plus a 1 / r^3 term that only kicks in very close to the body/black hole. I didn't see any reference to this in the linked answers. $\endgroup$ – m4r35n357 Oct 16 '20 at 8:33
  • $\begingroup$ @Qmechanic please see my comment! $\endgroup$ – m4r35n357 Oct 16 '20 at 8:33
  • $\begingroup$ @jamesraymond please see my comment $\endgroup$ – m4r35n357 Oct 16 '20 at 8:39