Anisotropic Stellar Models with Tolman IV Spacetime in Non-minimally Coupled Theory

Abstract

This article aims to investigate various anisotropic stellar models in the background of $f(\mathcal{R},\mathcal{T},\mathcal{Q})$ gravity, where $\mathcal{Q}={\mathcal{R}}_{\phi \vartheta }{\mathcal{T}}^{\phi \vartheta }$. In this regard, we adopt two standard models as $\mathcal{R}+\zeta \mathcal{Q}$ and $\mathcal{R}+\zeta \mathcal{R}\mathcal{Q}$, where $\zeta$ symbolizes an arbitrary coupling parameter. We take spherical interior geometry and find solution to the modified gravitational field equations corresponding to each model by employing the `Tolman IV' spacetime. We need an additional constraint to close the system of field equations, thus the $\mathbb{MIT}$ bag model equation of state is chosen. The effects of modified theory on physical properties of six compact stars like PSR J 1614 2230,~SMC X-1,~Cen X-3,~PSR J 1903+327,~SAX J 1808.4-3658 and 4U 1820-30 are analyzed by using their respective masses and radii. We also determine the values of three unknowns involving in Tolman IV solution as well as the bag constant for each star at the hypersurface. Furthermore, various characteristics of the resulting solutions are examined through graphical interpretation for $\zeta =\pm 5$. Finally, we explore the stability of the compact objects through two different approaches. We conclude that our model-I produces physically acceptable structures corresponding to each star candidate for both values of $\zeta$ whereas model-II is stable only for $\zeta =5$.

39 pages, 10 figures

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