ModMax model of nonlinear electrodynamics without the linear term

Abstract

The ModMax model of nonlinear electrodynamics (NED) is investigated in the absence of the linear term. The linear term is itself a ModMax model, however, the nonlinear term is not. First, in (3+1)-dimensional Minkowski spacetime, we introduce the electromagnetic theory in this NED model. We find the vacuum electric permittivity and magnetic permeability which both are in tensor form. This shows that the propagation of the speed of the electromagnetic wave depends on the direction. Finally, we couple our NED Lagrangian density minimally with the standard gravity and find a dyonic black hole solution.