General Relativity versus Dark Matter for rotating galaxies

TL;DR

This paper explores how general relativity can explain galaxy rotation curves without dark matter by analyzing axially-symmetric metrics and their implications for galaxy dynamics, angular momentum, and velocity plateaus.

Contribution

It introduces a class of extended Weyl metrics in GR that account for galaxy rotation, providing new insights into velocity profiles and angular momentum without dark matter.

Findings

GR rotational velocity exceeds Newtonian velocity due to Lenz's law.

Non-zero galaxy angular momentum implies constant Weyl parameter a.

Conditions for velocity plateaus and gauge laws derived within the extended Weyl framework.

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 ($J$) for a galaxy demands the asymptotic constancy of the Weyl (vectorial) length parameter ($a$) -a behavior identical to that found for the Kerr metric; (iii) Asymptotic constancy of the same parameter $a$ 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 \&\ $J$ for our own galaxy has been presented.