Non-Maxwellian electromagnetism in astrophysics

The universe is largely observed with electromagnetic signals ¿ supposedly Maxwellian ¿ though the gravitational wave window was just unbarred. Meanwhile, cosmology is since long confronted with an universe for 96% dark and unknown. Thus, it is pertinent for fundamental physics to start a theoretical and experimental verification of electromagnetism, and its photon messenger. The study discusses nonMaxwellian theories, focusing on testable effects. We deal with a range of applications and assess how alternative electromagnetic theories are helpful. We revise the most notable theories, either non-linear or massive. In the former class, for analysis of the self-force, we consider the radiation of an uniformly accelerating Born-Infeld charge; in the Heisenberg-Euler theory, we find a frequency shift induced by an overcritical magnetic dipole, associated to a magnetar. Being the photon the only massless particle in the Standard Model (SM), we explore SM extensions.