Coulomb Sectors and Scattering for Maxwell-Higgs Fields on Schwarzschild and Slowly Rotating Kerr Backgrounds
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| Format: | Preprint |
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2026
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| _version_ | 1866914610982944768 |
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| author | Gunara, Bobby Eka Mulyanto Akbar, Fiki Taufik |
| author_facet | Gunara, Bobby Eka Mulyanto Akbar, Fiki Taufik |
| contents | We develop a small-data Maxwell--Higgs theory on Schwarzschild and slowly rotating Kerr black-hole exteriors for gauge-invariant nonnegative self-interactions near the trivial vacuum. The Schwarzschild part gives a complete global, radiative, and scattering theory, while the slowly rotating Kerr part gives a robust massless forward theory and a perturbative small-electric extension. The main mechanism is a transfer principle: once the required linear energy, decay, horizon, and far-field estimates are available, the nonlinear Lorenz-gauge problem yields global existence, gauge-covariant radiation fields, nonlinear wave operators, and asymptotic completeness. The Coulomb-sector analysis identifies the correct long-range normalization in fixed electric sectors and separates the genuinely proved results from the remaining rotating massive final-state problems. All Kerr scattering statements beyond the established massless and small-electric forward regimes are stated explicitly under their necessary spectral and final-state conditions, namely, no rapid-rotation, large-charge, and unconditional massive rotating scattering. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_04202 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Coulomb Sectors and Scattering for Maxwell-Higgs Fields on Schwarzschild and Slowly Rotating Kerr Backgrounds Gunara, Bobby Eka Mulyanto Akbar, Fiki Taufik General Relativity and Quantum Cosmology High Energy Physics - Theory Mathematical Physics Analysis of PDEs 35Q61, 35L05, 83C57 We develop a small-data Maxwell--Higgs theory on Schwarzschild and slowly rotating Kerr black-hole exteriors for gauge-invariant nonnegative self-interactions near the trivial vacuum. The Schwarzschild part gives a complete global, radiative, and scattering theory, while the slowly rotating Kerr part gives a robust massless forward theory and a perturbative small-electric extension. The main mechanism is a transfer principle: once the required linear energy, decay, horizon, and far-field estimates are available, the nonlinear Lorenz-gauge problem yields global existence, gauge-covariant radiation fields, nonlinear wave operators, and asymptotic completeness. The Coulomb-sector analysis identifies the correct long-range normalization in fixed electric sectors and separates the genuinely proved results from the remaining rotating massive final-state problems. All Kerr scattering statements beyond the established massless and small-electric forward regimes are stated explicitly under their necessary spectral and final-state conditions, namely, no rapid-rotation, large-charge, and unconditional massive rotating scattering. |
| title | Coulomb Sectors and Scattering for Maxwell-Higgs Fields on Schwarzschild and Slowly Rotating Kerr Backgrounds |
| topic | General Relativity and Quantum Cosmology High Energy Physics - Theory Mathematical Physics Analysis of PDEs 35Q61, 35L05, 83C57 |
| url | https://arxiv.org/abs/2603.04202 |