Galactic Metrics

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2002-09-22

arxiv.org/abs/astro-ph/0209456v3

Gen.Rel.Grav.36:2423-2431,2004

Astronomy and Astrophysics

Astrophysics

7 pages - major revision

Scientific paper

10.1023/B:GERG.0000046830.85831.

The paths of stars in galaxies have circular velocity independent of their distance from the centre of the galaxy. Newtonian mechanics with a logarithmic potential has such paths. In relativity these paths can be taken to be geodesics and this requirement places a resticting equation on the spacetime metric. This equation has a non-unique spherically symmetric solution that in the newtonian limit has a logarithmic potential. It also can be solved in terms of a conformal factor. In particular it has solutions which are conformal to the vacuum-Einstein solutions and such spacetimes are solutions to the vacuum-Bach equations. Therefore it is suggested that the Bach equations describe dynamics on galactic lenght scales.

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