Born–Infeld theory of electromagnetism

Abstract The chapter begins with a discussion of the two classical formalisms of Born and Infeld of nonlinear electrodynamics, which were aimed historically to resolve the energy divergence problem of an electric point charge as a model for the electron. The chapter then extends the theory as it investigates a broad range of problems which include a mechanism to exclude monopoles, relegation and regularization of curvature singularities of black holes, and a k-essence realization of the equation of state for a perfect fluid model of the universe. A few related nonlinear partial differential equation problems are also considered along the lines.