A class of static spherically symmetric solutions in $f(T)$-gravity

TL;DR

This paper explores static spherically symmetric solutions in $f(T)$-gravity, including black holes, wormholes, and galaxy rotation curve models, by solving the field equations with constant torsion scalar.

Contribution

It introduces a specific class of solutions in $f(T)$-gravity with constant torsion scalar, analyzing their properties and potential astrophysical applications.

Findings

Found black hole solutions within the class.

Identified wormhole configurations compatible with the model.

Demonstrated potential to explain galaxy rotation curves.

Abstract

We study a class of static spherically symmetric vacuum solutions in modified teleparallel gravity solving the field equations for a specific model Ansatz, requiring the torsion scalar $T$ to be constant. We discuss the models falling in this class. After some general considerations, we provide and investigate local solutions in the form of black holes and traversable wormholes as well as configurations that can match the anomalous rotation curves of galaxies.