Exact charged black-hole solutions in D-dimensional f(T) gravity: torsion vs curvature analysis

TL;DR

This paper derives exact charged black-hole solutions in D-dimensional f(T) gravity, analyzing their singularities and horizons through torsion and curvature invariants, revealing differences in singularity structures especially when matter fields are involved.

Contribution

It provides explicit charged black-hole solutions in D-dimensional f(T) gravity and compares torsion and curvature invariants, highlighting their differing behaviors in the presence of matter.

Findings

Charged black-hole solutions with flat transverse sections are obtained.

Curvature invariants show more singularities than torsion invariants in some cases.

Differences between f(T) and f(R) gravity are emphasized when matter fields are present.

Abstract

We extract exact charged black-hole solutions with flat transverse sections in the framework of D-dimensional Maxwell-f(T) gravity, and we analyze the singularities and horizons based on both torsion and curvature invariants. Interestingly enough, we find that in some particular solution subclasses there appear more singularities in the curvature scalars than in the torsion ones. This difference disappears in the uncharged case, or in the case where f(T) gravity becomes the usual linear-in-T teleparallel gravity, that is General Relativity. Curvature and torsion invariants behave very differently when matter fields are present, and thus f(R) gravity and f(T) gravity exhibit different features and cannot be directly re-casted each other.