Numerical experiments with a regular charged black hole

In this work, we studied the Ayon-Beato Garcia (ABG) solution describing a nonsingular charged black hole using the moving-puncture method. As the first step, we obtained the BG solution in isotropic coordinates with a new, accurate numerical procedure. By focusing on the situation where there is at least one horizon, where the charge is smaller than or equal to a particular critical value, we show the transition between the wormhole geometry described by the isotropic solution to a time-independent trumpet foliation resulting from the disconnection of the two asymptotic regions of the wormhole geometry. The numerical experiments indicate that, as the charge approaches its critical value, the trumpet geometry approaches the extreme isotropic solution.