Abstract
Using the classical vacuum solutions of Newtonian gravity that do not explicitly involve matter, dark matter, or the gravitational constant, subject to an averaging process, a form of gravity relevant to the flattening of galaxy rotation curves results. The latter resembles the solution found if the vacuum is simply assigned a gravitational field density, and a volume of the vacuum is then excluded, with no averaging process. A rationale then follows for why these terms would become important on the galactic scale. Then, a modification of General Relativity, motivated by the Newtonian solutions, that are equivalent to a charge void, is partially defined and discussed in terms of a least action principle.
Highlights
ΛCDM is the standard cosmological model to which most physicists are committed
The galaxy circular velocity in the flat region is from (21) v ∝ MBH 3/2. This volume estimation is simplistic, as it assumes that the density of rotary charge in the vacuum is constant beneath the event horizon, while neglecting aspects concerning the physical volume due to the metric, and unknowns with how the vacuum interacts with it
It is suggested that the vacuum provides a uniform rotary charge density at all points in space, except beneath the event horizons of black holes at galactic centers, where the vacuum is suggested to not be able to contribute to a vector cancellation effect
Summary
ΛCDM is the standard cosmological model to which most physicists are committed. no dark matter particle has ever been observed, directly or indirectly [1,2,3,4,5,6,7,8]. The addition of a force term going as 1/r in Newtonian gravity to explain the observed flattening is not at all new, for example Kuhn in 1986 and the many references therein as far back as 1963 [14] It forms part of the basis for MOND. The solutions to be examined have always been available, starting with the vacuum solutions of classical, non-relativistic gravity This idea has already been examined by Zhang for a particular solution [15], with a compelling argument for why it is reasonable to add such terms (though without development of the specific source of effects), the most important of which is that the Einstein Field. A discussion concerning ways to puncture fields is given in terms of General Relativity and a least action principle
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