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.

**Author(s) Details**

**Günter Scharf
**Physics Institute, University of Zürich, Winterthurerstr. 190, CH‐8057 Zürich, Switzerland.

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