Post-Maxwellian electrodynamics with neutron stars

One of the big, open problems in gravity is whether or not black holes have singularities. In vacuum general relativity this is guaranteed via the Hawking-Penrose theorems, but by coupling to various nonlinear, electromagnetic Lagrangians it has been shown that charge may regularise the object.

Physically, this is argued to be because gravity is attractive and electrostatics repulsive, preventing singularities. Some highly-magnetised neutron stars ("magnetars") have inferred polar field strengths well in excess of the Schwinger limit, where nonlinear electromagnetic effects may dominate. Their internal fields may be even stronger, meaning that Maxwellian descriptions of hydromagnetic structure may require revision.

In Born-Infeld-like theories -- a popular candidate for regularizing holes -- I argue that the toroidal field has a maximum strength set by the scale parameter. Because of this, there is an implicit bound to the stellar prolateness which can be inferred via gravitational waves; detections or non-detections can thus be used to set bounds on post-Maxwellian parameters that is competitive with terrestrial experiments. Connections with black hole singularities
will then be made.