Unitary and finite self-energy of a massive classical point charge as a naked point singularity

Abstract

We analyze linear Einstein--Maxwell perturbations of the superextremal Reissner--Nordström geometry, the nonlinear self-field of a single static point charge, in its static Kerr--Schild rest frame. Using optical radial coordinates and gauge-invariant master variables, we reduce the radiative Einstein--Maxwell sectors to scalar wave equations on the half-line. The resulting master equations are of Regge--Wheeler type, with inverse-square potential cores at the optical apex and short-range tails at infinity. Hardy control at the apex, together with the short-range estimates at infinity, proves that the action-induced spatial $T$-energy forms are semibounded and closable. Closing these spatial forms determines their finite-energy configuration-form domains; adjoining the $L^2$ velocity components supplied by the kinetic energy gives the Cauchy-data energy spaces. The form representation theorem then yields the action-normalized Friedrichs Hamiltonians associated with the master operators. The static Coulomb field and its nonlinear gravitational backreaction are treated as the exact background. All radiative perturbations whose Cauchy data have finite total $T$-energy evolve uniquely and unitarily on the completed energy space. The naked singularity remains geometrically present but is dynamically silent: it carries no $T$-energy flux, supports no finite-energy bound state, and introduces no hidden finite-energy endpoint sector. We also construct the forward radiation field at future null infinity, obtaining a translation representation in which the conserved $T$-energy equals the squared $L^2$ norm of the radiation profile in retarded time.