From weak interaction to gravity

Abstract

We follow an old suggestion made by Stueckelberg that there exists an intimate connection between weak interaction and gravity, symbolized by the relationship between the Fermi and Newton’s constants. We analyze the hypothesis that the effect of matter upon the metric that represents gravitational interaction in general relativity is an effective one. This leads us to consider gravitation to be the result of the interaction of two neutral spinorial fields ([Formula: see text]-neutrinos) [Formula: see text] and [Formula: see text] with all kinds of matter and energy. We present three examples with only one [Formula: see text]-neutrino: two static and spherically symmetric configurations and a cosmological framework for an isotropic dynamical universe. Without self-interaction, the associated effective geometry is precisely the Schwarzschild metric. On the other hand, a self-interacting [Formula: see text]-neutrino generates a new gravitational black hole.

Galaxy rotation curves in the light of the Spinor Theory of Gravity

“…Recently [1,2], some of us have analyzed the hypothesis according to which gravity is controlled by spinor fields that combine in an effective metric. In that proposal, the main hypothesis of General Relativity (GR) that states that gravity may be interpreted as nothing but a modification of the geometry of the underlying space-time is followed.…”

“…[4]). In [1,2], a new program to consider an intimate connection between gravity and Fermi (weak) interaction has begun. As previously discussed in these papers, the main hypothesis of the Spinor Theory of Gravity relies upon a suggested connection between weak interactions and gravity, namely their high degree of universality, and the dimensional equivalence of their coupling constants in natural units system.…”

“…The coupling constant s has, in the natural units system c = = 1, dimesion of lenght squared. The associated gravitational effective metric [1] exhibits an intimate connection between weak interaction and gravity and it is given by…”

“…In the search of a static and spherically symmetric solutions of STG, we set for a self-interacting g-neutrino, (see Ref. [1]) Ψ(r) = f (r) Ψ 0 , such that the constant spinor can be decomposed as…”

“…Thus, after a change of coordinates, it follows for the light-like vector ∆ µ that ∆ 2 = ∆ 3 = 0 (see details in Ref. [1]). Finally, we arrive at the effective gravitational metric -experienced by all kind of matter in the case of a spherically symmetric and time-independent configuration -expressed in terms of the infinitesimal line element…”