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Most people assume that in order to have agreement between GR and the rotation curve of galaxies:

  1. GR isnt correct

  2. There is hidden matter which makes the galaxies rotate faster at their edges.

GR is a set of differential equations with only very few solutions known(Schwarzwild, Kerr metric, linearized GR) however why cant both GR be correct and the rotation of the galaxies be explained at the same time?

Maybe if we COULD have analytical solution of GR for every case , then we would see that the set of differential equations produce the rotation of the galaxies observed by our telescopes...

ZaellixA
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appliedSciences
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1 Answers1

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We don't need exact analytic solutions to understand a theory's predictions. General relativity in particular reduces to Newtonian gravity in the weak-field (and low-velocity) limit, which is where changes in the Newtonian gravitational potential $\Phi$ are much smaller than $c^2$ (and velocities are much smaller than $c$). General relativistic corrections to Newtonian gravity are suppressed by powers of $\Delta\Phi/c^2$ (and $v/c$, with the lowest velocity correction being at second order).

In galaxies, the potential depth $|\Phi|/c^2\sim 10^{-6}$, so Newtonian gravity is accurate to about one part in a million. This is why we are satisfied with using Newtonian gravity to model galaxies.

See also How can we recover the Newtonian gravitational potential from the metric of general relativity?

Sten
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