Can Einstein's equations fully explain gravitational anomalies in galaxies?

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Are the anomalous galactic rotation curves and observed gravitational lensing(i.e.bullet cluster) not well explained only when using Newtonian theory or has this problem also been tried out with Einstein field equations? ( I guess it is hard to deal with GR non-linear equations since it implies many bodies)
 
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Good question. Differentially rotating discs of dust can be described in GR, see Ansorg and Meinel, "Differentially rotating disks of dust" (1999) arXiv:gr-qc/9910045v2. This has been recently extended to include a BH at the centre. But I haven't found any attempt to calculate the rotation curves.
 

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