For cylindrical black strings, NED Lagrangians with a Maxwell weak-field limit cannot produce regular purely electric or dyonic cores; regular magnetic Bardeen/Hayward analogues exist but violate causality near the axis.
Nonlinear electrodynamics as a symmetric hyperbolic system
2 Pith papers cite this work. Polarity classification is still indexing.
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abstract
Nonlinear theories generalizing Maxwell's electromagnetism and arising from a Lagrangian formalism have dispersion relations in which propagation planes factor into null planes corresponding to two effective metrics which depend on the point-wise values of the electromagnetic field. These effective Lorentzian metrics share the null (generically two) directions of the electromagnetic field. We show that, the theory is symmetric hyperbolic if and only if the cones these metrics give rise to have a non-empty intersection. Namely that there exist families of symmetrizers in the sense of Geroch which are positive definite for all covectors in the interior of the cones intersection. Thus, for these theories, the initial value problem is well-posed. We illustrate the power of this approach with several nonlinear models of physical interest such as Born-Infeld, Gauss-Bonnet and Euler-Heisenberg.
fields
gr-qc 2years
2026 2representative citing papers
Regular black-hole and black-bounce solutions are derived in lower-dimensional EGB gravity using nonlinear electrodynamics or unimodular extensions, with thermodynamics showing modified evaporation, remnants, and phase transitions.
citing papers explorer
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On regular black string spacetimes in nonlinear electrodynamics
For cylindrical black strings, NED Lagrangians with a Maxwell weak-field limit cannot produce regular purely electric or dyonic cores; regular magnetic Bardeen/Hayward analogues exist but violate causality near the axis.
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Geometrically Regular Black Object Solutions in Lower-Dimensional Gauss-Bonnet Gravity and Its Unimodular Extension
Regular black-hole and black-bounce solutions are derived in lower-dimensional EGB gravity using nonlinear electrodynamics or unimodular extensions, with thermodynamics showing modified evaporation, remnants, and phase transitions.