New physical parameterizations of monopole solutions in five-dimensional general relativity and the role of negative scalar field energy in vacuum solutions

Abstract

Abstract Novel parameterizations are presented for monopole solutions to the static, spherically-symmetric vacuum field equations of five-dimensional general relativity. First proposed by Kaluza, 5D general relativity unites gravity and classical electromagnetism with a scalar field. These monopoles correspond to bodies carrying mass, electric charge, and scalar charge. The new parameterizations provide physical insight into the nature of electric charge and scalar field energy. The Reissner-Nordström limit is compared with alternate physical interpretations of the solution parameters. The new parameterizations explore the role of scalar field energy and the relation of electric charge to scalar charge. The Kaluza vacuum equations imply the scalar field energy density is the negative of the electric field energy density for all known solutions, so the total electric and scalar field energy of the monopole is zero. The vanishing of the total electric and scalar field energy density for vacuum solutions seems to imply the scalar field can be understood as a negative-energy foundation on which the electric field is built.