General Relativity versus Dark Matter for rotating galaxies
Abstract
A very general class of axially-symmetric metrics in general relativity (GR) that includes rotations is used to discuss the dynamics of rotationally-supported galaxies. The exact vacuum solutions of the Einstein equations for this extended Weyl class of metrics allow us to deduce rigorously the following: (i) GR rotational velocity always exceeds the Newtonian velocity (thanks to Lenz's law in GR); (ii) A non-vanishing intrinsic angular momentum () for a galaxy demands the asymptotic constancy of the Weyl (vectorial) length parameter () -a behavior identical to that found for the Kerr metric; (iii) Asymptotic constancy of the same parameter also demands a plateau in the rotational velocity. Unlike the Kerr metric, the extended Weyl metric can and has been continued within the galaxy and it has been shown under what conditions Gau\ss\ \&\ Amp\'ere laws emerge along with Ludwig's extended GEM theory with its attendant non-linear rate equations for the velocity field. Better estimates (than that from the Newtonian theory) for the escape velocity of the Sun and a reasonable rotation curve \&\ for our own galaxy has been presented.
Cite
@article{arxiv.2207.04279,
title = {General Relativity versus Dark Matter for rotating galaxies},
author = {Yogendra Srivastava and Giorgio Immirzi and John Swain and Orland Panella and Simone Pacetti},
journal= {arXiv preprint arXiv:2207.04279},
year = {2023}
}
Comments
22 pages, 4 figures; v2, minor corrections, e-mails added