This paper has some great ideas about gravitational field self-interaction in a modest modification of General Relativity. The author has published two prior papers exploring the same theory.
Modified General Relativity (MGR) is the natural extension of General Relativity (GR). MGR explicitly uses the smooth regular line element vector field (X, - X), which exists in all Lorentzian spacetimes, to construct a connection-independent symmetric tensor that represents the energy-momentum of the gravitational field.
It solves the problem of the non-localization of gravitational energy-momentum in GR, preserves the ontology of the Einstein equation, and maintains the equivalence principle. The line element field provides MGR with the extra freedom required to describe dark energy and dark matter. An extended Schwarzschild solution for the matter-free Einstein equation of MGR is developed, from which the Tully-Fisher relation is derived, and the gravitational energy density is calculated.
The mass of the invisible matter halo of galaxy NGC 3198 calculated with MGR is identical to the result obtained from GR using a dark matter profile. Although dark matter in MGR is described geometrically, it has an equivalent representation as a particle with the property of a vector boson or a pair of fermions; the geometry of spacetime and the quantum nature of matter are linked together by the unit line element covectors that belong to both the Lorentzian metric and the spin-1 Klein-Gordon wave equation.
The three classic tests of GR provide a comparison of the theories in the solar system and several parts of the cosmos. MGR provides the flexibility to describe inflation after the Big Bang and galactic anisotropies.
Gary Nash, "Modified General Relativity and dark matter" arXiv:2304.09671 (April 19, 2023) (International Journal of Modern Physics D related publication here).
"Thus, a massive neutral vector boson and a
ReplyDeletepair of neutral neutrinos with a presently unknown mass are viable candidates for a particle theory of dark
matter. There is no conflict between the geometrical and particle descriptions of dark matter because the
unit line element covectors of the Lorentzian metric satisfy the Klein-Gordon wave equation that describes
spin-1 particles."
The massive neutral vector boson is postulated to be a "dark photon"
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