Finite energy and momentum of time-dependent Maxwell–Born–Infeld solutions with accelerated point charges

Establish whether time-dependent solutions of the Maxwell–Born–Infeld field equations, in the presence of accelerated point charge sources, possess finite total field energy and momentum.

Background

The paper reviews foundational issues in classical electrodynamics and contrasts nonlinear Maxwell–Born–Infeld (MBI) theory with linear Bopp–Landé–Thomas–Podolsky (BLTP) theory. While electrostatic MBI solutions with point charges are known to exist and have finite energy, the status of time-dependent MBI solutions under acceleration remains unsettled. Determining finiteness of energy and momentum for such solutions is a key step toward validating MBI as a consistent classical field theory with point sources.

This question concerns global properties of solutions under dynamical evolution and is distinct from BLTP, which the authors paper in detail here. Resolving it would clarify whether MBI avoids pathological infinities (beyond the static case) when charges are accelerated.

References

it is still not rigorously known whether time-dependent solutions of these field equations do have finite field energy and momentum when the point charge sources are accelerated.

— Radiation-Reaction on the Straight-Line Motion of a Point Charge accelerated by a constant applied Electric Field in an Electromagnetic Bopp-Landé-Thomas-Podolsky vacuum (2506.08799 - McGuigan et al., 10 Jun 2025) in Section 1 (Introduction)