# Regular Reissner-Nordstr\"om black hole solutions from linear electrodynamics

## TL;DR

This paper demonstrates that certain regular black hole metrics, previously attributed to nonlinear electrodynamics, can also be derived from Einstein's equations coupled with linear electromagnetism, under specific energy conditions.

## Contribution

It shows that regular Reissner-Nordström black holes can be obtained from linear electromagnetism, expanding the understanding of their physical sources beyond nonlinear theories.

## Key findings

- Regular black hole metrics can be interpreted as solutions of Einstein-Maxwell equations.
- Singularities are replaced by regular charged fluid spheres within the inner horizon.
- The effective energy-momentum tensor satisfies the dominant energy condition.

## Abstract

In recent years there have appeared in the literature a large number of static, spherically symmetric metrics, which are regular at the origin, asymptotically flat, and have both an event and a Cauchy horizon for certain range of the parameters. They have been interpreted as regular black hole (BH) spacetimes, and their physical source attributed to electric or magnetic monopoles in a suitable chosen nonlinear electrodynamics. Here we show that these metrics can also be interpreted as exact solutions of the Einstein equations coupled to ordinary linear electromagnetism{\textemdash}i.e., as sources of the Reissner-Nordstr\"om (RN) spacetime{\textemdash}provided the components of the effective energy-momentum tensor satisfy the dominant energy condition (DEC). We use some well-known regular BH metrics to construct nonsingular RN black holes, where the singularity at the RN center is replaced by a regular perfect fluid charged sphere (whose charge-to-mass ratio is not greater than $1$) which is inside the RN inner horizon.