2004-11
AUTHORS ABSTRACTThe 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 restricting 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 length scales. More... »
PAGES2423-2431
http://scigraph.springernature.com/pub.10.1023/b:gerg.0000046830.85831.4a
DOIhttp://dx.doi.org/10.1023/b:gerg.0000046830.85831.4a
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