Regular Article - Theoretical Physics
General relativity versus dark matter for rotating galaxies
Emeritus Professor of Physics, Northeastern University, Boston, MA, USA
2 Dipartimento di Fisica e Geologia, Università di Perugia, Perugia, Italy
3 Physics Department, Northeastern University, Boston, MA, USA
4 Istituto Nazionale di Fisica Nucleare, INFN Sezione di Perugia, Perugia, Italy
Accepted: 12 November 2022
Published online: 31 January 2023
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 rigorously deduce 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 behaviour 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 Gauß and Ampére laws emerge along with Ludwig’s extended gravito-electromagnetism (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 have been presented.
© The Author(s) 2023
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