New spherically symmetric monopole and regular solutions in Einstein–Born–Infeld theories

DIEGO JULIO CIRILO-LOMBARDO

JOURNAL OF MATHEMATICAL PHYSICS

AMER INST PHYSICS

Año: 2005 vol. 46 p. 42501 - 42515

0022-2488

In this work a new asymptotically flat solution of the coupled Einstein–Born–Infeld equations for a static spherically symmetric space–time is obtained. When the intrinsic mass is zero the resulting space–time is regular everywhere, in the sense given by Hoffmann and Infeld in 1937, and the Einstein–Born–Infeld theory leads to the identification of the gravitational with the electromagnetic mass. This means that the metric, the electromagnetic field, and their derivatives do not have discontinuities in all the manifold. In particular, there are not conical singularities at the origin, in contrast to the well-known monopole solution studied by Hoffmann in 1935. The lack of uniqueness of the action function in nonlinear electrodynamics is discussed