Regular Black Holes and Stars from Analytic $f(F^2)$

TL;DR

This paper constructs regular black holes and stars within Einstein-$f(F^2)$ gravity, exploring their properties, energy conditions, duality symmetries, and geodesic behaviors, revealing novel solutions that challenge traditional energy condition constraints.

Contribution

The paper introduces new analytic $f(F^2)$ functions for regular black holes and stars, develops electromagnetic duality formalism, and provides explicit examples with unique properties.

Findings

Regular black holes violate the strong energy condition.

A regular black hole with Minkowski core violates the null energy condition.

Duality transformations can be symmetries in certain $f(F^2)$ models.

Abstract

We construct regular black holes and stars that are geodesically complete and satisfy the dominant energy condition from Einstein-$f(F^2)$ gravities with several classes of analytic $f(F^2)$ functions that can be viewed as perturbations to Maxwell's theory in weak field limit. We establish that regular black holes with special static metric ($g_{tt} g_{rr}=-1$) violate the strong energy condition and such a regular black hole with Minkowski core violates the null energy condition. We develop a formalism to perform electromagnetic duality transformations in $f(F^2)$. We obtain two new explicit examples where the duality is a symmetry. We study the properties of the corresponding dyonic black holes. We study the geodesic motions of a particular class of solutions that we call repulson stars or black holes.