# A Perturbative Approach to Neutron Stars in $f(T, \mathcal{T})-$Gravity

## TL;DR

This paper develops a perturbative method to derive the structure equations of neutron stars within a modified gravity framework called $f(T, \, \mathcal{T})$-gravity, incorporating a polytropic equation of state to analyze mass and density relations.

## Contribution

It introduces a perturbative approach to formulate neutron star equations in $f(T, \, \mathcal{T})$-gravity using a tetrad formalism and derives mass profiles under a polytropic equation of state.

## Key findings

- Derived a modified Tolman-Oppenheimer-Volkoff equation for $f(T, \mathcal{T})$-gravity.
- Established mass-central density relations for neutron stars in this gravity model.
- Provided a framework for analyzing neutron stars in alternative gravity theories.

## Abstract

We derive a Tolman-Oppenheimer-Volkoff equation in neutron star systems within the modified $f(T, \mathcal{T})$-gravity class of models using a perturbative approach. In our approach $f(T, \mathcal{T})$-gravity is considered to be a static spherically symmetric space-time. In this instance the metric is built from a more fundamental tetrad vierbein which can be used to relate inertial and global coordinates. A linear function $f = T(r) + \mathcal{T}(r) + \chi h(T, \mathcal{T}) + \mathcal{O}(\chi^{2})$ is taken as the Lagrangian density for the gravitational action. Finally we impose the polytropic equation of state of neutron star upon the derived equations in order to derive the mass profile and mass-central density relations of the neutron star in $f(T, \mathcal{T})$-gravity.