A study of anisotropic spheres in $f(Q)$ gravity with quintessence field

TL;DR

This paper investigates anisotropic compact star models within $f(Q)$ gravity incorporating a quintessence field, analyzing their physical viability, stability, and matching conditions for specific star candidates.

Contribution

It introduces a new $f(Q)$ gravity model with quintessence, derives solutions for anisotropic stars, and assesses their physical and stability properties.

Findings

Solutions are physically feasible and stable.

Models satisfy energy and causality conditions.

Good agreement with observed compact star properties.

Abstract

This manuscript examines the compact stars in gravity $f (Q)$, where non-metricity $Q$ drives gravitational interactions. To achieve this goal, we consider a spherically symmetric spacetime with the anisotropic fluid distribution. In particular, the quintessence field is used in the energy-momentum tensor to explore the solution of compact stars. In addition, we select three specific types of compact stars, namely HerX-1, SAXJ1808.4-3658, and 4U1820-30. We develop the field equations using the quintessence field of a specific form of $f(Q)$ as $f(Q)=Q-\alpha \gamma \left(1-\frac{1}{e^{\frac{Q}{\gamma}}}\right)$ in $f (Q)$ gravity. In addition, we consider the Schwarzschild metric for the matching conditions at the boundary. Then, we calculate the values of all the relevant parameters by imposing matching conditions. We provide detailed graphical analyses to discuss the parameters' physical viability, namely energy density, pressure, gradient and anisotropy. We also examine the stability of compact stars by testing energy conditions, equations of state, conditions of causality, redshift functions, mass functions, and compactness functions. Finally, we find that the solutions we obtained are physically feasible in modified $f (Q)$ gravity, and also it has good properties for the compact star models.