Extensible gravitational Dirac models of the electron

Abstract

Various gravitational extensions of Dirac's extensible model of the electron are discussed. First we consider two different models involving a thin dynamical brane which either (i) matches two Reissner–Nordström regimes, or (ii) matches an exterior Reissner–Nordström with an interior de Sitter core. Positive surface tension and a novel vector field localized on the brane (necessarily in a magnetic monopole-like configuration) serve as a source for the electrically charged configuration in the bulk. Underlying the equations of motion of the spherically symmetric brane is a variation principle originally introduced by Dirac in the case of a non-dynamical flat background. The gravitational extension of Dirac's variation prescription is crucial for our analysis; its major effect is to induce an additional contribution to the brane energy–momentum tensor. As a result, the effective potential which governs the evolution of the bubble's radius exhibits a local minimum, and furthermore, the set of parameters involved allows us to avoid the so-called classical radius of the electron problem. Finally, we demonstrate that our main conclusions stay valid in the Kaluza–Klein generalization, where a Z2 symmetric matching of two five-dimensional Chodos–Detweiler vacuum solutions is performed in the Dirac style.