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Introductory Notes on Non-linear Electrodynamics and its Applications
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In 1933-1934 Born and Infeld constructed the first non-linear generalization of Maxwell's electrodynamics that turned out to be a remarkable theory in many respects. In 1935 Heisenberg and Euler computed a complete effective action describing non-linear corrections to Maxwell's theory due to quantum electron-positron one-loop effects. Since then, these and a variety of other models of non-linear electrodynamics proposed in the course of decades have been extensively studied and used in a wide range of areas of theoretical physics including string theory, gravity, cosmology and condensed matter (CMT). In these notes I will overview general properties of non-linear electrodynamics and particular models which are distinguished by their symmetries and physical properties, such as a recently discovered unique non-linear modification of Maxwell's electrodynamics which is conformal and duality invariant. I will also sketch how non-linear electromagnetic effects may manifest themselves in physical phenomena (such as vacuum birefringence), in properties of gravitational objects (e.g. charged black holes) and in the evolution of the universe, and can be used, via gravity/CMT holography, for the description of properties of certain conducting and insulating materials.
Forward citations
Cited by 21 Pith papers
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Excising Cauchy Horizons with Nonlinear Electrodynamics
For nonlinear electrodynamics with finite point-charge self-energy and strong energy condition, weakly charged black holes have Schwarzschild-like causal structure with no Cauchy horizon.
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Degenerate higher-order Maxwell-Einstein theories
A complete classification of quadratic degenerate Maxwell-Einstein theories is given, including a new theory that generalizes Horndeski's non-minimal coupling to gauge fields.
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Thermodynamics of charged and accelerating black holes
For charged accelerating AdS black holes in Maxwell, ModMax, and RegMax theories, topological renormalization of the Euclidean action differs from holographic renormalization by 2πℓ²μ₊T when the total cosmic string te...
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The Euler-Heisenberg action for a $U(1)\times U(1)$ dyon quantum electrodynamics
One-loop Euler-Heisenberg Lagrangian for U(1)×U(1) dyon QED produces hybrid refractive indices and vacuum birefringence that reduce exactly to ordinary QED when magnetic charge vanishes.
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Quasitopological Gravity with Matter: Modified Double-Copy Approach
Spherically symmetric quasitopological gravity with matter is mapped exactly to a flat-space nonlinear gauge theory in D+1 dimensions, with the Einstein limit giving Maxwell theory.
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Probing nonlinear electrodynamics-sourced black holes via light and orbital mechanics
For ModMax black holes, Shapiro time delay and gravitational redshift are identical for both photon polarizations, while Sagnac and kinematic shifts distinguish them; S2 precession bounds e^-gamma (Q/2M)^2 <= 0.135.
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A causal magnetic black hole with finite self-energy
A positive power-kernel mixture in nonlinear electrodynamics yields an exact magnetic black hole whose metric is strictly increasing for nonnegative mass parameter, giving at most one horizon and no inner Cauchy horiz...
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Purely Electric, Magnetic, and Dyonic Black Holes in Einstein-Euler-Heisenberg Theory
In Einstein-Euler-Heisenberg theory, purely magnetic and mixed electric-magnetic black holes can have three horizons, one outer and two inner, for weak QED coupling.
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Orbital Motion in Spacetimes Influenced by the Presence of Scalar and Electromagnetic Fields
Strong scalar fields around naked singularities can create stable circular orbits, and charged scalar-field spacetimes can host both stable and unstable photon orbits.
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Conformal geometry as a gauge theory of gravity: covariant equations of motion & conservation laws
The most general Weyl-quadratic-gravity action yields manifestly gauge-covariant equations of motion, with energy-momentum and Weyl-current conservation holding in both the Weyl and Riemannian pictures.
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Vaidya-Type Solutions of Quasitopological Gravity Interacting with Nonlinear Electrodynamics
Radiating (Vaidya-type) charged black holes in quasitopological gravity are generated from static ones by promoting mass and charge to functions of time, with the required currents and radiation fluxes constructed explicitly.
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An obstruction and residual-completion theory for Newman--Janis deformations
Newman–Janis rotations of black-hole seeds are treated as off-shell ansätze whose failure is measured by an obstruction tensor, with a residual-completion criterion deciding when a correction can make them solve the f...
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Nonlinear electrodynamics and stability of spherically symmetric space-times in scalar-tensor gravity
For NED with Maxwell weak-field limit, monopole stability of STT solutions with F=0 is identical to Maxwell-STT, and the zero-charge limit of V_eff erases all NED traces.
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Scalarization of Einstein-Euler-Heisenberg black hole with multiple horizons
Stable, positive-mass scalarized EEH black holes exist only in an intermediate primary-scalar-charge window for low/cold horizons and above a lower bound for hot horizons.
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Generalised Symmetries and Manifest Duality I: Flat Spacetime
A proposed manifestly Lorentz-invariant duality-symmetric action reduces, after removing auxiliary fields, to two independent Maxwell theories rather than a single photon or self-dual sector.
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Negative potential-induced scalarization in the Einstein-Euler-Heisenberg black hole
A single branch of scalarized Einstein-Euler-Heisenberg black holes is constructed numerically, found to be thermodynamically disfavored and dynamically unstable for all magnetic charges.
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Constraining ModMax Black Holes with EHT and GRAVITY Observations: Optical Signatures and Accretion Disk Properties
Combining EHT shadow observations of M87* and Sgr A* with mass and distance priors yields 95% upper limits Q < 0.391 and v < 4.153 on the ModMax black hole charge and nonlinearity parameter.
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Optical and orbital characterization of spherically symmetric static black holes of self-gravitating new nonlinear electrodynamics model
PINLED Y^n black holes have charge-driven inward shifts of photon sphere, shadow, and ISCO, with null-geodesic observables distinguishing them from RN more clearly than timelike ones.
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Scattering and absorption of massless scalar waves by a ModMax black hole
Massless scalar-wave scattering and absorption cross sections for ModMax black holes are computed and shown to reproduce the Reissner-Nordström limit with an effective screened charge.
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Barotropic Equation of State and Nonlinear Electrodynamics in Dynamical Black Hole Spacetimes
The paper's identification of the Husain solution's integration constant with nonlinear electrodynamics charges is undermined by internal inconsistencies in the reconstruction.
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Formation of regular black hole from baryonic matter
A family of regular black hole collapse solutions is built by imposing a de Sitter core and matching to a Husain exterior; the shadow radius grows with the barotropic parameter alpha.
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