Generalization of Regular Black Holes in General Relativity to $f(R)$ Gravity

TL;DR

This paper constructs regular black hole solutions within a broad $f(R)$ gravity framework coupled with non-linear electromagnetic fields, ensuring regularity and satisfying most energy conditions, with some violations near horizons.

Contribution

It introduces a general method to derive regular black hole solutions in $f(R)$ gravity without specifying the functions explicitly, using a mass function approach.

Findings

Solutions exhibit two horizons: event and Cauchy horizons.

All energy conditions are satisfied except SEC near the Cauchy horizon.

Solutions maintain regular geometric invariants.

Abstract

In this paper, we determine regular black hole solutions using a very general $f(R)$ theory, coupled to a non-linear electromagnetic field given by a Lagrangian $\mathcal{L}_{NED}$. The functions $f(R)$ and $\mathcal{L}_{NED}$ are left in principle unspecified. Instead, the model is constructed through a choice of the mass function $M(r)$ presented in the metric coefficients. Solutions which have a regular behaviour of the geometric invariants are found. These solutions have two horizons, the event horizon and the Cauchy horizon. All energy conditions are satisfied in the whole space-time, except the strong energy condition (SEC) which is violated near the Cauchy horizon.