Charge Without Charge, Regular Spherically Symmetric Solutions and the Einstein-Born-Infeld Theory

Abstract

The aim of this paper is to continue the research (J. Math. Phys. 46:042501, 2005) of regular static spherically symmetric spacetimes in Einstein-Born-Infeld theories from the point of view of the spacetime geometry and the electromagnetic structure. The energy conditions, geodesic completeness and the main features of the horizons of this spacetime are explicitly shown. A new static spherically symmetric dyonic solution in Einstein-BornInfeld theory with similar good properties as in the regular pure electric and magnetic cases of our previous work, is presented and analyzed. Also, the circumvention of a version of "no go" theorem claiming the non existence of regular electric black holes and other electromagnetic static spherically configurations with regular center is explained by dealing with a more general statement of the problem. The Regularity ProblemLast years considerable interest in regular black hole solutions has been renewed [13], and in particular, to those based in nonlinear electrodynamics (NED) [3,11]. In our previous work [6] we presented a new exact spherically symmetric solution of the Einstein-BornInfeld (EBI) equations. The metric is regular everywhere in the sense that was given by B. Hoffmann and L. Infeld [15] in 1937 and, when the intrinsic mass of the system is zero, the EBI theory leads to identification of the gravitational with the electromagnetic mass. Explicitly the line element that we obtained in [6] is ds 2 = −e 2 dt 2 + e 2F(r) e −2 (1 + r∂ r F (r)) 2 dr 2 + r 2 (dθ 2 + sin 2 θdϕ 2 ) ,