General relativity versus dark matter for rotating galaxies

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 foll...

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Bibliographic Details
Published in:The European physical journal. C, Particles and fields Particles and fields, 2023-01, Vol.83 (1), p.100-15, Article 100
Main Authors: Srivastava, Yogendra, Immirzi, Giorgio, Swain, John, Panella, Orlando, Pacetti, Simone
Format: Article
Language:English
Subjects:
Angular momentum
Astronomy
Astrophysics and Cosmology
Asymptotic properties
Dark matter
Einstein equations
Electromagnetism
Elementary Particles
Escape velocity
Galactic rotation
Galaxies
Hadrons
Heavy Ions
Laws, regulations and rules
Mathematical analysis
Measurement Science and Instrumentation
Nuclear Energy
Nuclear Physics
Parameters
Physics
Physics and Astronomy
Quantum Field Theories
Quantum Field Theory
Regular Article - Theoretical Physics
Relativity
Rotating matter
Stars & galaxies
String Theory
Theory of relativity
Velocity
Velocity distribution
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Summary: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.
ISSN:1434-6052
1434-6044
1434-6052
DOI:10.1140/epjc/s10052-022-11031-3