Equivalence between two charged black holes in dynamics of orbits outside the event horizons

TL;DR

This paper compares the dynamics of charged particles around two similar black holes, showing their gravitational systems behave equivalently outside the horizons despite differences in their internal structures.

Contribution

It demonstrates the approximate equivalence of the dynamical properties of two charged black holes with different internal structures in the region outside the event horizons.

Findings

Both black holes have similar photon orbits and effective potentials.

Chaotic dynamics increase with magnetic field strength and negative Coulomb parameters.

The Reissner-Nordstrom black hole can be effectively replaced by a regular black hole in many scenarios.

Abstract

Using the FermiDirac distribution function, Balart and Vagenas gave a charged spherically symmetric regular black hole, which is a solution of Einstein field equations coupled to a nonlinear electrodynamics. In fact, the regular black hole is a Reissner-Nordstrom (RN) black hole when a metric function is given a Taylor expansion to first order approximations. It does not have a curvature singularity at the origin,but the RN black hole does. Both black hole metrics have horizons and similar asymptotic behaviors, and satisfy the weak energy conditions everywhere. They are almost the same in photon effective potentials, photon circular orbits and photon spheres outside the event horizons. There are relatively minor differences between effective potentials, stable circular orbits and innermost stable circular orbits of charged particles outside the event horizons of the two black holes immersed in external magnetic fields. Although the twomagnetized black holes allow different construction methods of explicit symplectic integrators, they exhibit approximately consistent results in the regular and chaotic dynamics of charged particles outside the event horizons. Chaos gets strong as the magnetic field parameter or the magnitude of negative Coulomb parameter increases, but becomes weak when the black hole charge or the positive Coulomb parameter increases. A variation of dynamical properties is not sensitive dependence on an appropriate increase of the black hole charge. The basic equivalence between the two black hole gravitational systems in the dynamics of orbits outside the event horizons is due to the two metric functions having an extremely small difference. This implies that the RN black hole is reasonably replaced by the regular black hole without curvature singularity in many situations.