Solving Tolman-Oppenheimer-Volkoff equations in $f(T)$ gravity: a novel approach applied to polytropic equations of state

TL;DR

This paper develops a numerical method to solve Tolman-Oppenheimer-Volkoff equations within $f(T)$ gravity, applying it to polytropic equations of state to analyze neutron star properties and compare with General Relativity.

Contribution

It introduces a novel approach to solve TOV equations in $f(T)$ gravity for polytropic EOSs, enabling comparison with GR and exploration of higher maximum neutron star masses.

Findings

Reproduces known GR results for neutron stars.

Identifies $f(T)$ models that predict higher maximum masses.

Provides a framework for future realistic EOS analysis.

Abstract

The Teleparallel Theory is an alternative theory of gravity equivalent to General Relativity (GR) and with non-vanishing torsion $T$. Some extensions of this theory, the so-called $f(T)$ models, have been subject of many recent works. The purpose of our work in the end is to consider recent results for a specific family of $f(T)$ models by using their corresponding Tolman-Oppenheimer-Volkof to describe compact objects such as neutron stars. By performing numerical calculations, it is possible to find, among other things, the maximum mass allowed by the model for a neutron star for a given equation of state (EOS), which would also allow us to evaluate which models are in accordance with observations. To begin with, the present work, the second in the series, considers polytropic EOSs since they can offer a simpler and satisfactory description for the compact objects. In addition, with these EOSs, we can already assess how different the $f(T)$ theories are in relation to GR with respect to the stellar structure. The results already known to GR must be reproduced to some extent and, eventually, we can find models that allow higher maximum masses than Relativity itself, which could explain, for example, the secondary component of the event GW190814. This particular issue will be subject of a forthcoming paper, the third in the series, where realistic EOSs are considered.