Hexadecapole at the heart of nonlinear electromagnetic fields
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866929415399669760 |
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| author | Bokulić, Ana Jurić, Tajron Smolić, Ivica |
| author_facet | Bokulić, Ana Jurić, Tajron Smolić, Ivica |
| contents | In classical Maxwell's electromagnetism, monopole term of the electric field is proportional to $r^{-2}$, while higher order multipole terms, sourced by anisotropic sources, fall-off faster. However, in nonlinear electromagnetism even a spherically symmetric field has multipole-like contributions. We prove that the leading subdominant term of the electric field, defined by nonlinear electromagnetic Lagrangian obeying Maxwellian weak field limit, in a static, spherically symmetric, asymptotically flat spacetime, is of the order $O(r^{-6})$ as $r \to \infty$. Moreover, using Lagrange inversion theorem and Faà di Bruno's formula, we derive the series expansion of the electric field from the Taylor series of an analytic electromagnetic Lagrangian. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_08909 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Hexadecapole at the heart of nonlinear electromagnetic fields Bokulić, Ana Jurić, Tajron Smolić, Ivica General Relativity and Quantum Cosmology High Energy Physics - Theory Mathematical Physics In classical Maxwell's electromagnetism, monopole term of the electric field is proportional to $r^{-2}$, while higher order multipole terms, sourced by anisotropic sources, fall-off faster. However, in nonlinear electromagnetism even a spherically symmetric field has multipole-like contributions. We prove that the leading subdominant term of the electric field, defined by nonlinear electromagnetic Lagrangian obeying Maxwellian weak field limit, in a static, spherically symmetric, asymptotically flat spacetime, is of the order $O(r^{-6})$ as $r \to \infty$. Moreover, using Lagrange inversion theorem and Faà di Bruno's formula, we derive the series expansion of the electric field from the Taylor series of an analytic electromagnetic Lagrangian. |
| title | Hexadecapole at the heart of nonlinear electromagnetic fields |
| topic | General Relativity and Quantum Cosmology High Energy Physics - Theory Mathematical Physics |
| url | https://arxiv.org/abs/2403.08909 |