Unitary and finite self-energy of a single classical point charge and naked point singularity spacetimes
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arXiv
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| Formato: | Preprint |
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2025
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| _version_ | 1866912917621833728 |
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| author | Delucchi, Daxx W. |
| author_facet | Delucchi, Daxx W. |
| contents | We analyze linear Einstein--Maxwell perturbations of the superextremal Reissner--Nordström geometry in its static Kerr--Schild rest frame, viewing it as the nonlinear self-field of a single static point charge. In optical radial coordinates, and using the Kodama--Ishibashi gauge-invariant formalism, each radiative multipole is encoded by a single scalar master field on the half-line. The resulting master equation is of Regge--Wheeler type, with an inverse-square potential core at the optical apex (controlled by a Hardy inequality) and a short-range tail at infinity. The spatial-plus-potential part of the Einstein--Maxwell $T$-energy is closable and bounded below, which defines a positive quadratic form on the natural energy space. Its Friedrichs extension then gives the canonical self-adjoint realization of the master operator. The static Coulomb field and its nonlinear gravitational backreaction are treated as the exact background. All linear Einstein--Maxwell perturbations with finite spatial $T$-energy evolve unitarily on the energy space. The naked singularity at finite optical distance is ``silent'' in the technical sense that it carries no $T$-energy flux. We also construct the forward radiation field at future null infinity, obtaining a translation representation of the self-field dynamics in which the conserved $T$-energy coincides with the $L^2$ norm of the radiation profile in retarded time. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_19015 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Unitary and finite self-energy of a single classical point charge and naked point singularity spacetimes Delucchi, Daxx W. General Relativity and Quantum Cosmology Mathematical Physics 83C57, 35P25 We analyze linear Einstein--Maxwell perturbations of the superextremal Reissner--Nordström geometry in its static Kerr--Schild rest frame, viewing it as the nonlinear self-field of a single static point charge. In optical radial coordinates, and using the Kodama--Ishibashi gauge-invariant formalism, each radiative multipole is encoded by a single scalar master field on the half-line. The resulting master equation is of Regge--Wheeler type, with an inverse-square potential core at the optical apex (controlled by a Hardy inequality) and a short-range tail at infinity. The spatial-plus-potential part of the Einstein--Maxwell $T$-energy is closable and bounded below, which defines a positive quadratic form on the natural energy space. Its Friedrichs extension then gives the canonical self-adjoint realization of the master operator. The static Coulomb field and its nonlinear gravitational backreaction are treated as the exact background. All linear Einstein--Maxwell perturbations with finite spatial $T$-energy evolve unitarily on the energy space. The naked singularity at finite optical distance is ``silent'' in the technical sense that it carries no $T$-energy flux. We also construct the forward radiation field at future null infinity, obtaining a translation representation of the self-field dynamics in which the conserved $T$-energy coincides with the $L^2$ norm of the radiation profile in retarded time. |
| title | Unitary and finite self-energy of a single classical point charge and naked point singularity spacetimes |
| topic | General Relativity and Quantum Cosmology Mathematical Physics 83C57, 35P25 |
| url | https://arxiv.org/abs/2602.19015 |