Finch–Skea quintessence models in non-conservative theory of gravity

This study is dedicated to presenting a new solution of the field equations in the Rastall theory with a quintessence field defined by the parameter ${\omega }_q$ as $-1<{\omega }_q<-\frac{1}{3}$ by considering the isotropic matter content inside the sphere. The Finch–Skea ansatz ($FS$) is used in a static and spherically symmetric geometry to obtain the feasible relativistic solution. The results obtained in the physical evaluation are analyzed analytically and graphically. In the appropriate limit of the Rastall coupling parameter, one can regain the original results in the General Relativity. This complete analysis considers five different compact stars: $HerX-1$ with mass $0.88M_{\odot }$ and radius 7.7 km, $VelaX-12$ with mass $1.77M_{\odot }$ and radius 9.99 km, $SAXJ1808-3658\left(SSI\right)$ with mass $1.435M_{\odot }$ and radius 7.07 km, $4U1608-52$ with mass $1.74M_{\odot }$ and radius 9.30 km, $4U1538-52$ with mass $0.87M_{\odot }$ and radius 7.86 km and $PSRJ1416-2230$ with mass $1.97M_{\odot }$ and radius 10.30 km. The physical validity of the obtained solution is verified by computing the necessary physical parameters like energy density and pressure, quintessence density, energy conditions, sound speed via the Herrera cracking concept, hydrostatic equilibrium of forces, mass function, compactness, Buchdahl limit, and surface redshift and analyze their behavior graphically. To investigate the demeanor of these parameters more closely, we computed the numerical values and manifested them in tabular form. We conclude that our presented mathematical model of compact stars in the Finch–Skea geometry with quintessence field fulfills all the requirements for a physically viable solution.