# Advances in Astrophysics

### Island Universes: Galactic General Relativity without Dark Matter

Download PDF (368.6 KB) PP. 63 - 74 Pub. Date: August 1, 2020

### Author(s)

**Günter Scharf**^{*}

Physics Institute, University of Zürich, Winterthurerstr. 190 , CH-8057 Zürich, Switzerland

### Abstract

We apply the perturbative technique which was previously developed in cosmology to
now describe the gravitational field of a galaxy with arbitrary rotation curve. The rotation curve
fixes the background metric. We use a Schwarzschild background as starting point, however with
the correct physical coordinates. Then 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 explains the structure of disk galaxies with a bulge. As the
inverse of the standard procedure the theory predicts the matter distribution for a given rotation
curve. For small distances the rotation curve is Keplerian, so that the usual Schwarzschild metric
and the classical Solar System tests follow.

### Keywords

galactic general relativity, dark matter.

### References

[1] Scharf G.2016, Gauge Field Theories, Spin 1 and Spin 2, 100 Years After General Relativity, Dover Publications, Inc. Mineola, New York

[2] De Jong R.S. Editor, Island Universes,Structure and Evolution of Disk Galaxies, 2007 Springer

[3] Scharf G. 2018, Cosmology with the cosmic rest frame, arXiv 1503.05878

[4] Scharf G. 2019, Perturbation theory in nonstandard cosmology, Adv. Astrophys. 4(4), 133, arXiv 1905.02526

[5] Scharf G. 2020. Cosmology without dark matter, Adv.Astrophys. 5(1), 1

[6] Regge T., Wheeler J.A. 1957, Physical Review 108, 1063

[7] Müller O., Pawlowski M.S., Jerjen H., Lelli F. 2018, Science 359, 534