Abstract
We demonstrate that the total energy of electromagnetic field in the Bardeen and Ay\'on-Beato-Garc\'ia singularity-free models is equal to the mass parameter $M$, being therefore independent of the charge parameter $Q$. Our result is fully congruent with the original idea of Born and Infeld to use nonlinear electrodynamics for proving the electromagnetic nature of mass.
Highlights
The construction of regular black hole models was pioneered by Bardeen [1] who ingeniously modified the well-known Reissner-Norstrom metric [2, 3] for spherically symmetric mass and charge to remove the singularity at r = 0
Being strongly convinced that the answer to this question must be closely related to the issue of electromagnetic energy associated with the above spacetimes, in the present letter we will calculate the total electromagnetic energy in the Bardeen and ABG models to reveal that for all these models it has the same value that does not depend on the charge parameter Q
It is really surprising that all three different models of non-singular black-hole spacetimes considered in the present paper share the same fundamental characteristic with regard to the issue of the total electromagnetic energy whose value, on the one hand, turns out to be independent of the charge parameter Q and, on the other hand, is equal exactly to the ADM mass M
Summary
The construction of regular black hole models was pioneered by Bardeen [1] who ingeniously modified the well-known Reissner-Norstrom metric [2, 3] for spherically symmetric mass and charge to remove the singularity at r = 0. The first exact regular black hole solutions were constructed, within the framework of Einstein’s gravity coupled to nonlinear electrodynamics, by Ayon-Beato and Garcıa [5, 6] who later reinterpreted Bardeen’s model as an exact solution for a nonlinear magnetic monopole [7]. Despite a considerable attention these solutions have received in recent years, it seems that the main physical question concerning the Bardeen and ABG spacetimes – How can an arbitrarily small charge remove the physical Schwarzschild singularity of a collapsed star with enormous mass? Being strongly convinced that the answer to this question must be closely related to the issue of electromagnetic energy associated with the above spacetimes, in the present letter we will calculate the total electromagnetic energy in the Bardeen and ABG models to reveal that for all these models it has the same value that does not depend on the charge parameter Q
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