# Quark Stars in $f(T, \mathcal{T})-$Gravity

## TL;DR

This paper develops a modified gravity model based on $f(T, \\mathcal{T})$-gravity to analyze quark star structures, deriving the TOV equations, and explores mass-radius relations using the MIT bag model.

## Contribution

It introduces a new $f(T, \\mathcal{T})$-gravity framework for quark stars and derives the corresponding TOV equations with specific linear models.

## Key findings

- Derived TOV equations for quark stars in $f(T, \\mathcal{T})$-gravity.
- Analyzed mass-radius relations using the MIT bag model.
- Outlined restrictions on coupling parameters in the modified gravity model.

## Abstract

We derive a working model for the Tolman-Oppenheimer-Volkoff equation for quark star systems within the modified $f(T, \mathcal{T})$-gravity class of models. We consider $f(T, \mathcal{T})$-gravity for a static spherically symmetric space-time. In this instance the metric is built from a more fundamental tetrad vierbein from which the metric tensor can be derived. We impose a linear $f(T)$ parameter parameter, namely taking $f=\alpha T(r) + \beta \mathcal{T}(r) + \varphi$ and investigate the behavior of a linear energy-momentum tensor trace, $\mathcal{T}$. We also outline the restrictions which modified $f(T, \mathcal{T})$-gravity imposes upon the coupling parameters. Finally we incorporate the MIT bag model in order to derive the mass-radius and mass-central density relations of the quark star within $f(T, \mathcal{T})$-gravity.