Dark Matter and Equivalence Principle Dark Matter effects show up in galaxies. Why isn't it considered as a violation of equivalence principle instead of assuming all these extra non-interacting particles as gravitational mass and inertial mass are equal to a great extent but the effect will show up in case of extremely large bodies like galaxies when all these individual errors are added up.
 A: The equivalence principle is a principle of general relativity. General relativity has survived other experimental tests and solves many theoretical problems. Do if galaxy rotation seems to violate the theory, it is worth trying to come up with a way to save it.
The standard approach to galaxy rotation uses a Newtonian approximation to general relativity. Dark matter theorists propose that there is an additional form of matter that makes this model match reality.
Some theories, such as Modified Newtonian Dynamics, modify the Newtonian approximation to account for the rotation. MOND proposes that the Newtonian approximation breaks at low accelerations. There is a relativistic version of MOND called TeVeS, which satisfies the equivalence principle:
https://arxiv.org/abs/astro-ph/0403694,
but it doesn't explain the rotation curves.
There are suggestions for ways of reconciling the rotation curves with general relativity that differ from the Newtonian approximation for large bound systems:
https://arxiv.org/abs/1101.3224.
This may eliminate the need for dark matter at some point, or not.
