We apply the perturbative technique which was previously developed in cosmology to now describe
the gravitational field of a galaxy with arbitrary rotation curve. We use a Schwarzschild background as
starting point, however with the correct physical coordinates. In the perturbation theory we find two
classes of metric perturbations, (i) stationary perturbations in a 3‐dimensional vicinity of the central
black hole and (ii) non‐stationary perturbations in an infinitely thin disk. Since the metric perturbations
directly give the matter density the theory so explains the structure of disk galaxies with a bulge.
Physics Institute, University of Zürich, Winterthurerstr. 190, CH‐8057 Zürich, Switzerland.
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