Study on physical properties and maximum mass limit of Finch-Skea anisotropic model under Karmarkar condition in $f(Q)$-gravity

TL;DR

This paper investigates the physical properties and maximum mass limits of anisotropic compact stars within $f(Q)$ gravity, using the Karmarkar condition and Finch-Skea model, supported by observational data and stability analysis.

Contribution

It introduces a novel approach combining $f(Q)$ gravity, Karmarkar condition, and Finch-Skea structure to model anisotropic stars and derive their mass-radius relations.

Findings

Mass-radius relation derived for different densities.

Maximum mass limits identified for various parameters.

Stability and physical viability confirmed through graphical analysis.

Abstract

The primary objective of this work is to study the dynamical characteristics of an anisotropic compact star model with spherical symmetry. This investigation is conducted in the framework of $f(Q)$ modified gravity. To simplify the calculations, we employ the Karmarkar condition and derive a differential equation that establishes a relationship between two crucial components of the spacetime namely $e^\nu$ and $e^\lambda$. Additionally, we incorporate the well-known Finch-Skea structure as the component representing $g_{rr}$ and subsequently find the resulting form of the component $g_{tt}$ from the relation of metric functions to formulate the precise solutions for the stellar structure. To assess the behavior of the anisotropic fluid and stability of the compact star, we use the observed values of mass and radius for the compact star model $PSR J0437-4715$. The graphical analysis depicts that the stellar structure possesses physical viability and exhibits intriguing properties. Furthermore, we predicted the mass-radius relation along with the maximum mass limit of several objects for different parameter values by assuming two different surface densities. It is discovered that the compactness rises when density increases.