General Relativity coupled with Non-Linear Electrodynamics: results and limitations

TL;DR

This paper explores how non-linear electrodynamics can generate black hole solutions in General Relativity, analyzes their thermodynamics, and discusses the limitations of NED for modeling regular black holes.

Contribution

It provides a general mechanism for generating NED black hole solutions and examines their thermodynamic properties, highlighting limitations of NED for regular black holes.

Findings

NED solutions can be generated by solving algebraic equations.

Thermodynamics of NED black holes follows the First Law.

NED may not be optimal for studying regular black holes.

Abstract

We discuss how to generate a black hole solution of the Einstein Equations (EE) via non-linear electrodynamics (NED). We discuss the thermodynamical properties of a general NED solution, recovering the First Law. Then we illustrate the general mechanism and discuss some specific cases, showing that finding a generating Lagrangian (for a specific solution) only requires solving an algebraic equation (we study some analytical cases). Finally, we argue that NED paradigm, though self-consistent, is not the best tool for studying regular black holes.