Born-Infeld field theory with external sources and gravitational generalization

It is stated that the external sources of a field are to be introduced into the Born-Infeld nonlinear electrodynamics. A version of the Born-Infeld theory with external sources (currents) is considered in a flat space-time, in analogy with the Maxwell-Lorentz electrodynamics. It is concluded that in a consistent theory the bare mass and charge of a nonfield origin should exist. The theory with external sources is formulated in the framework of gravitational generalization. An analog of the Birkhoff theorem is proved. The investigation of the spherically-symmetric static solution for a point source has revealed an essential singularity at the point of the source. Solutions are found of the type of a ''black hole'' with horizon and of the type of a naked singularity. A nonsingular self-consistent solution is obtained by introducing an extended source of charge and mass