# A note on singular and non-singular black holes

## TL;DR

This paper examines the conditions under which black holes can be singular or non-singular within General Relativity coupled with nonlinear electromagnetic sources, proposing a reconstruction method and exploring new solutions.

## Contribution

It introduces a reconstruction method for black hole solutions and discusses new non-singular black hole models within the framework.

## Key findings

- Singular contributions can still exist in static spherically symmetric solutions.
- A reconstruction method for black hole metrics is proposed.
- New non-singular black hole solutions are presented.

## Abstract

An attempt is made in order to clarify the so called regular black holes issue. It is revisited that if one works within General Relativity minimally coupled with non linear source, mainly of electromagnetic origin, and within a static spherically symmetric ansatz for the metric, there is still room for singular contribution to the black hole solution. A reconstruction method is proposed and several examples are discussed, including new ones. A possible way to obtain a non singular black hole is introduced, and in this case, several known examples are re-discussed, and new ones are provided.