Palatini $f(R)$ Black Holes in Nonlinear Electrodynamics

TL;DR

This paper investigates how certain Palatini $f(R)$ gravity models alter the structure and singularities of Born-Infeld black holes, revealing significant differences from General Relativity near the core.

Contribution

It provides a detailed analysis of electrically charged Born-Infeld black holes within Palatini $f(R)$ theories, highlighting modifications in horizon structure and singularity behavior.

Findings

Black holes differ from GR near the center.

Central singularities are shifted or weakened.

Divergence of curvature scalars is altered.

Abstract

The electrically charged Born-Infeld black holes in the Palatini formalism for $f(R)$ theories are analyzed. Specifically we study those supported by a theory $f(R)=R\pm R^2/R_P$, where $R_P$ is Planck's curvature. These black holes only differ from their General Relativity counterparts very close to the center, but may give rise to different geometrical structures in terms of inner horizons. The nature and strength of the central singularities are also significantly affected. In particular, for the model $f(R)=R - R^2/R_P$ the singularity is shifted to a finite radius, $r_+$, and the Kretschmann scalar diverges only as $1/(r-r_+)^{2}$.