Different coordinate frames for static axisymmetric vacuum spacetimes produce different effective potentials and rotation curves for low-velocity local observers.
General Relativity Resolves Galactic Rotation Without Exotic Dark Matter
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A galaxy is modeled as a stationary axially symmetric pressure-free fluid in general relativity. For the weak gravitational fields under consideration, the field equations and the equations of motion ultimately lead to one linear and one nonlinear equation relating the angular velocity to the fluid density. It is shown that the rotation curves for the Milky Way, NGC 3031, NGC 3198 and NGC 7331 are consistent with the mass density distributions of the visible matter concentrated in flattened disks. Thus the need for a massive halo of exotic dark matter is removed. For these galaxies we determine the mass density for the luminous threshold as 10^{-21.75} kg.m$^{-3}.
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On Coordinate Frames in Axisymmetric Static Vacuum Spacetimes and Implications for Observations
Different coordinate frames for static axisymmetric vacuum spacetimes produce different effective potentials and rotation curves for low-velocity local observers.