On the electromagnetic self-force in Bopp-Podolsky electrodynamics and gravitational interactions

For many classical applications in plasma physics and accelerator science it is reasonable to model moving charges in terms of collections of charged point particles.

Therefore a physically acceptable and mathematically consistent theory of classical charged point particles is desirable.

In classical Maxwell theory the self-force of a charged point particle is infinite.

This makes classical mass renormalization necessary and leads to the Abraham-Lorentz-Dirac equation of motion possessing unphysical run-away and pre-acceleration solutions.

I will outline a higher order modification of classical Maxwell vacuum electrodynamics  suggested originally by Bopp, Lande and Podolski and show how it can be developed to construct a theory with a finite self-force without classical mass renormalisation.

By formulating an action for the theory in a curved spacetime one can derive the Hilbert stress-energy-momentum tensor for generalised Maxwell fields coupled to Einsteinian gravitation and deduce that all Einstein-Maxwell solutions are also solutions to the Einstein-Bopp-Lande-Podolsky field equations.

This leads to the conjecture that the theory may also admit regular black-hole solutions.