Estimating the Role of Bag Constant and Modified Theory on Anisotropic Stellar Models
Tayyab Naseer, M. Sharif
TL;DR
This work investigates anisotropic compact stars within the generalized gravity framework $f(\mathcal{R},\mathcal{T},\mathcal{Q})$ with $\mathcal{Q}=\mathcal{R}_{\alpha\gamma}\mathcal{T}^{\alpha\gamma}$, focusing on two coupling models and using the Finch-Skea spacetime together with the MIT bag model EoS $P_r=\tfrac{1}{3}(\rho-4\mathrm{B_c})$ to model strange quark matter. The field equations are derived for the two models, revealing non-minimal coupling and resulting in an effective energy–momentum tensor; the interior solutions are constructed by fixing the Finch-Skea triplet $(d_1,d_2,d_3)$ through surface matching to Schwarzschild geometry and a boundary condition $P_r(R)=0$. Graphical analysis for a specific star, 4U 1820-30, demonstrates physically viable, stable interiors for a chosen bag constant $\mathrm{B_c}=92\,\mathrm{MeV/fm^3}$ and explores the role of the coupling parameter $\beta$; the approach is then extended to constrain $\beta$ using observational data from eight compact-star candidates. Overall, the results indicate that the proposed models can yield physically acceptable anisotropic interiors consistent with observational constraints, highlighting the utility of non-minimal matter–geometry coupling in modeling dense stellar objects.
Abstract
In this article, we are devoted to discuss different compact stars admitting anisotropic interiors in a particular modified theory of gravity. For this purpose, a spherically symmetric metric is adopted to formulate the field equations corresponding to two different $f(\mathcal{R},\mathcal{T},\mathcal{Q})$ models, where $\mathcal{Q}=\mathcal{R}_{αγ}\mathcal{T}^{αγ}$. Since the field equations contain extra degrees of freedom, we choose Finch-Skea metric and MIT bag model equation of state to make them solvable. We also use matching conditions to calculate a constant triplet in the chosen ansatz. The resulting solutions are then graphically analyzed for particular values of the bag constant and model parameter in the interior of 4U 1820-30 compact star. The viability and stability of the modified models are also checked through certain tests. Further, we calculate the values of model parameter through the vanishing radial pressure constraint that correspond to the observed data (radii and masses) of eight different star candidates. Finally, we conclude that our models I and II are in well-agreement with the conditions needed for physically relevant interiors to exist.