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As I understand it, Modified Newtonian Dynamics, or MOND (Milgrom M., 1983, ApJ, 270, 365), slightly alters Newton's Law of Gravity by introducing a low acceleration limit below which (for an object in a circular orbit) the velocity no longer depends on the distance from the CM but rather only on the total mass of the system. As we know, Newtonian Gravity is the low-speed, weak-field limit of General Relativity. If MOND were found to be true, then it seems General Relativity would be inaccurate for certain systems. If MOND, not General Relativity, is the (more) accurate theory of gravity, what does that imply for the geometrical description of gravity as curved spacetime? Is that still valid?

For example, scientists have detected gravitational waves that were predicted by General Relativity. I assume that if MOND does not incorporate curved spacetime, then gravitational waves would technically conflict with it. However, this doesn't seem likely, since the discovery of gravitational waves has been widely confirmed and accepted, and MOND is still being researched.

What am I missing?

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    $\begingroup$ Related: physics.stackexchange.com/q/6561/2451 and links therein. $\endgroup$
    – Qmechanic
    Commented Jun 22, 2021 at 14:37
  • $\begingroup$ We know from classical mechanics that 1/r force laws are associated to a line source (cylindrical symmetry). I think one can incorporate MOND's empirical (1/r) force in GR by modelling space-time close to cylindrical symmetry (say, in a weak field limit, close to boundary of galaxy). However, the stress energy tensor corresponding to such metrics may not have a direct physical analogue (like, what kind of energy or matter distribution can sustain a cylindrically symmetric space-time?) GR itself is such a successful theory as a classical gravity theory and I think it has ample scopes. $\endgroup$
    – paul230_x
    Commented Jul 4, 2021 at 8:42

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General relativity is not the only possible theory of gravity, it is just the simplest such theory - or at least the simplest such theory that works. For many decades people have suggested modifications to GR by tweaking it or adding extra features and there is a long list of such theories in the Wikipedia article Alternatives to general relativity.

The original MOND theory from Milgrom is not generally covariant, but it has been made so by incorporating it into a theory called TeVeS. This is an extension of general relativity in the sense that it includes the action from GR but adds extra terms so it. TeVeS predicts much the same as GR in the scenarios we can test, as indeed it must do to be a viable theory, but it also matches the predictions of MOND.

So it isn't the case that if MOND were true it would invalidate general relativity, rather that GR would become an approximation that worked most of the time but would need the extra complexity of TeVeS outside the regimes where GR was a good approximation.

For the record we should note that dozens (literally) of alternatives to GR have come and gone but so far GR has survived every attempt to challenge it.

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I disagree that gr has survived every attempt to challenge it. Dark matter and dark energy seem more and more like the ether for light, that they just doesn't exist and we should modify gr even further to account for our observations

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    $\begingroup$ Dark energy is a very natural part of general relativity. Einstein himself was already waffling forth and back whether he should include the cosmological constant into the theory. Dark matter is not a challenge to GR at all. It's gravity is weak and its sources move at non-relativistic velocities, i.e. it can be modeled just fine with Newtonian gravity and mechanics. $\endgroup$ Commented Apr 14, 2023 at 15:54

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