Hexadecapole at the heart of nonlinear electromagnetic fields

Abstract

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.

arXiv comment9 pages (published version; one footnote added and one sentence expanded)

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Cited by in corpus (2)

• Conundrum of regular black holes with nonlinear electromagnetic fields
• Noncommutative dyonic black holes sourced by nonlinear electromagnetic fields