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Galactic Metrics

Mark D. Roberts
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Abstract

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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Mark D. Roberts. 2002-12-17. Galactic Metrics. https://doi.org/10.1023/b%3Agerg.0000046830.85831.4a

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