Four Parametric Regular Black Hole Solution

TL;DR

This paper introduces a new class of exact, regular black hole solutions in Einstein gravity coupled with nonlinear electrodynamics, characterized by four parameters, which generalize the Reissner-Nordström solution and satisfy energy conditions under certain parameters.

Contribution

The authors present a novel four-parameter family of regular black hole solutions that extend known solutions and satisfy physical energy conditions for specific parameter ranges.

Findings

Solutions are regular charged black holes for certain parameter values.

The solutions reduce to Reissner-Nordström when parameters are zero.

Some solutions satisfy the weak energy condition for specific parameters.

Abstract

We present a regular class of exact black hole solutions of Einstein equations coupled with a nonlinear electrodynamics source. For weak fields the nonlinear electrodynamics becomes the Maxwell theory, and asymptotically the solutions behave as the Reissner-Nordstr\"om one. The class is endowed with four parameters, which can be thought of as the mass $m$, charge $q$, and a sort of dipole and quadrupole moments $\alpha$ and $\beta$, respectively. For $\alpha \geq 3$, $\beta \geq 4$, and $|q| \leq 2 s_c m$ the corresponding solutions are regular charged black holes. For $\alpha=3$, they also satisfy the weak energy condition. For $\alpha=\beta=0$ we recover the Reissner-Nordstr\"om singular solution and for $\alpha=3$, $\beta=4$ the family includes a previous regular black hole reported by the authors.