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Is it true that the predictions from the General Theory of Relativity don’t match the observations of galaxy rotation speeds, and that this then started the search for dark matter? Is it only the rotation speeds of galaxies that are in conflict with GR or are there other observations that that don’t match the predictions as well?

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  • $\begingroup$ No, that is not correct. GR matches observations for certain dark matter distributions. $\endgroup$ – m4r35n357 Aug 17 '18 at 17:21
  • $\begingroup$ @m4r35n357 It only matches if there is dark matter? $\endgroup$ – Lambda Aug 17 '18 at 17:25
  • $\begingroup$ For those interested, this video addresses the topic well. youtu.be/fUAzc1evIBo $\endgroup$ – Lambda Aug 17 '18 at 18:05
  • $\begingroup$ we have to choose a matter distribution to use the GR theory. If things don't match, we can find a matter distribution that fixes it. This is the predictive power of GR. So if GR is correct then the matter distribution must be so-and-so. This is a falsifiable prediction, and makes GR a useful theory. $\endgroup$ – m4r35n357 Aug 17 '18 at 18:34
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General Relativity has nothing to do with the galaxy orbital speed. General relativity describes strong gravitational fields and the global geometry of spacetime. However, in the limit of the weak field, General Relativity simply matches the Newtonian gravity since the Newtonian gravity already matches the observation for the weak field.

Because gravity on the galactic scale is extremely weak, the orbital speed contradiction is with the Newtonian gravity. There is no direct contradiction with General Relativity, but only through the Newtonian gravity. It is not conceptually impossible that one day someone finds some additional initial or border conditions or some other conditions that would make General Relativity at the galactic scale different from the Newtonian gravity thus resolving the contradiction.

Currently there are two main approaches to resolve this issue. One is to assume the existence of the Dark Matter. The pros are that this assumption explains the observations, including Gravitational Lensing. The cons are that the dark matter itself has not been observed and currently is not a part of the Standard Model of elementary particles. Another approach is modifying the Newtonian gravity on the galactic scale. One such an attempt is known as MOND or Modified Newtonian Dynamics. The pros are that the unobserved dark matter is not required. The cons are that the observational evidence is not fully explained and no obvious fundamental theoretical basis for the modification.

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  • $\begingroup$ I liked that description of MOND. It's fairly impartial, but makes you realize that the pros really don't balance out those cons very well. It made me laugh. $\endgroup$ – Jim Aug 17 '18 at 18:22
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    $\begingroup$ "General Relativity is assumed to match the Newtonian gravity" - It is not merely an assumption that General Relativity matches Newtonian Gravity in the weak field limit. The correspondence can be shown mathematically, see e.g. Wald section 4.4 $\endgroup$ – enumaris Aug 17 '18 at 18:33
  • $\begingroup$ All my comments above should be read as pertaining to Newtonian physics too of course. So, if predictions do not match measurements we have two approaches: either we change model parameters to fit the data, or we can change the entire model. I would choose the former, unless GR or Newton(!) is falsified by some other means. $\endgroup$ – m4r35n357 Aug 17 '18 at 18:41
  • $\begingroup$ @enumaris Thanks for the clarification. I've updated the answer. We just need to assume no field at the infinite distance, but the reverse square does come from the Schwarzchild metric. $\endgroup$ – safesphere Aug 17 '18 at 18:50

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