Galactic Metrics
Astrophysics
2011-04-04 v3 General Relativity and Quantum Cosmology
High Energy Physics - Theory
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.
Keywords
Cite
@article{arxiv.astro-ph/0209456,
title = {Galactic Metrics},
author = {Mark D. Roberts},
journal= {arXiv preprint arXiv:astro-ph/0209456},
year = {2011}
}
Comments
7 pages - major revision