Solving Tolman-Oppenheimer-Volkoff equations in $f(T)$ gravity: a novel approach

TL;DR

This paper develops a numerical method to solve the Tolman-Oppenheimer-Volkoff equations within $f(T)$ gravity, enabling modeling of neutron stars without assuming specific metric forms or perturbations, and assesses model viability against observations.

Contribution

It introduces a direct numerical approach to solve TOV equations in $f(T)$ gravity for compact stars, avoiding prior assumptions on metric functions or perturbative methods.

Findings

Derived explicit equations for $f(T)$ gravity neutron star modeling

Demonstrated the numerical solution process for these equations

Enabled evaluation of maximum neutron star mass in $f(T)$ models

Abstract

The torsion models have stood out among the proposals for an alternative description of gravity. The simplest of them, the Teleparallel theory, is equivalent to General Relativity and there are many studies that seek to study its extension to more general functions of the torsion $T$. The purpose of {our study } is to consider a family of $f(T)$ models and apply their corresponding Tolman-Oppenheimer-Volkof equations to compact objects such as neutron stars. Consequently, through a numerical analysis, calculate, among other things, the maximum mass allowed by the model for a neutron star, which would also allow us to evaluate which models are in accordance with observations. In the present paper, the first in the series, we show explicitly the set of equations that must be solved, and how to solve it, in order to model compact stars in $f(T)$ gravity without the need to adopt any particular form for the metric functions or consider any perturbative approach, as has been done in some works in the literature.