Asymptotically anomalous black hole configurations in gravitating nonlinear electrodynamics

TL;DR

This paper classifies and analyzes asymptotically flat solutions in gravitating nonlinear electrodynamics, revealing conditions for physical admissibility and completing the understanding of point-like charge configurations.

Contribution

It provides a complete characterization and classification of elementary solutions in gravitating nonlinear electrodynamics with asymptotic flatness, including non-Schwarzschild-like configurations.

Findings

Energy positivity ensures asymptotic flatness of solutions.

Complete classification of elementary solutions in the studied models.

Extension of previous work to non-Schwarzschild-like solutions.

Abstract

We analyze the class of non-linear electrodynamics minimally coupled to gravitation supporting asymptotically flat \textit{non Schwarzschild-like} elementary solutions. The Lagrangian densities governing the dynamics of these models in flat space are defined and fully characterized as a subclass of the set of functions of the two standard field invariants, restricted by requirements of regularity, parity invariance and positivity of the energy, which are necessary conditions for the theories to be physically admissible. Such requirements allow for a complete characterization and classification of the geometrical structures of the elementary solutions for the corresponding gravity-coupled models. In particular, an immediate consequence of the requirement of positivity of the energy is the asymptotic flatness of gravitating elementary solutions for any admissible model. The present analysis, together with the (already published) one concerning the full class of admissible gravitating non-linear electrodynamics supporting asymptotically flat \textit{Schwarzschild-like} elementary solutions, completes and exhausts the study of the gravitating point-like charge problem for this kind of models.