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

TL;DR

This paper presents new regular, asymptotically flat solutions in Einstein-Born-Infeld theory, showing that for zero intrinsic mass, the spacetime is smooth and free of singularities, contrasting with earlier monopole solutions.

Contribution

It introduces novel spherically symmetric solutions in Einstein-Born-Infeld theory with regular spacetime and explores the implications of non-uniqueness in Non-Linear Electrodynamics.

Findings

Solutions are regular everywhere with no conical singularities.

The spacetime is asymptotically flat and the electromagnetic and gravitational masses are identified.

The solutions differ from earlier monopole models by Hoffmann and Infeld.

Abstract

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 spacetime is regular everywhere, in the sense given by B. Hoffmann and L. 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 have not discontinuities in all the manifold. In particular, there are not conical singularities at the origin, in contrast to well known monopole solution studied by B. Hoffmann in 1935. The lack of uniqueness of the action function in Non-Linear-Electrodynamics is discussed.