Relativistic model of anisotropic star with Bose-Einstein density depiction in $f(T)$ gravity

TL;DR

This paper develops a new relativistic model for anisotropic compact stars within $f(T)$ gravity, incorporating Bose-Einstein dark matter density and bag model EoS, demonstrating physical viability and stability.

Contribution

It introduces a novel anisotropic star model in $f(T)$ gravity with Bose-Einstein dark matter, satisfying physical conditions and matching observed compact star properties.

Findings

Model satisfies energy and causality conditions.

Maximum mass and surface redshift within realistic ranges.

Corresponds to observed compact objects like LMC X-4 and Her X-1.

Abstract

This article presents a new model for anisotropic compact stars that are confined to physical dark matter in the background of $f(T)$ teleparallel gravity. The model is based on the equation of state (EoS) of the bag model type and the Bose-Einstein dark matter density profile. The derived solutions meet the energy conditions, the causality conditions, and the required conditions on the stability factor and adiabatic index, indicating that they are physically well-behaved and represent the physical and stable matter configuration. We also determine the maximum mass, surface redshift, and compactness parameter at the surface. Interestingly, all of these numbers fall within the specified range, supporting the physical viability of our proposal. Additionally, the various masses that are derived for varying the model parameter $k$ correspond to five compact, realistic compact objects, including LMC X-4, Her X-1, 4U 1538-52, SAX J1808.4-3658, and Cen X-3. We have also illustrated the radially symmetric profiles of energy density and the moment of inertia for non-rotating stars.