Stable States of a Scalar Particle in Its Own Gravational Field

Abstract

Structures similar to classical geons are constructed using a matter field described by the Klein-Gordon equation. The matter field creates a gravitational field which interacts with the matter. The coupled system has stable, bound states. A spectrum of states is shown to exist with masses of the order of ${10}^{\ensuremath{-}10}$ kg. A variational principle is derived which is in precise analogy with the Rayleigh-Ritz principle of conventional quantum mechanics.