Some uniqueness results for stationary solutions to the Maxwell-Born-Infeld field equations and their physical consequences

Abstract

Uniqueness results are established for time-independent finite-energy electromagnetic fields which solve the nonlinear Maxwell--Born--Infeld equations in boundary-free space under the condition that either the charge or current density vanishes. In addition, it is also shown that the simpler Maxwell--Born equations admit at most a unique stationary finite-energy electromagnetic field solution, without the above condition. In these theories of electromagnetism, the following physical consequences emerge: source-free field solitons moving at speeds less than the vacuum speed of light $c$ do not exits; any purely electrostatic (resp. magnetostatic) field is the unique stationary electromagnetic field for the same current-density-free (resp. charge-density-free) sources. Our results put to rest some interesting speculations in the recent physics literature.

revised version, streamlined to 13 pages; theorems strengthened; 4 references added; submitted for publication

References in corpus (7)

• The Nonlinear Stability of the Trivial Solution to the Maxwell-Born-Infeld System
• On the Static Spacetime of a Single Point Charge
• Exploring Born-Infeld electrodynamics using plasmas
• Standstill Electric Charge Generates Magnetostatic Field Under Born-Infeld Electrodynamics
• Convergent perturbative power series solution of the stationary Maxwell--Born--Infeld field equations with regular sources
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Cited by in corpus (6)

• Global Structure of Five-dimensional BPS Fuzzballs
• Second gradient electromagnetostatics: electric point charge, electrostatic and magnetostatic dipoles
• When Fields Are Not Degrees of Freedom
• Two-dimensional solutions for Born-Infeld fields
• Approximated solutions to Born-Infeld dynamics
• Stochastic Evolution of Augmented Born--Infeld Equations