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.