Anisotropic Durgapal-Fuloria Neutron Stars in $f(\mathcal{R},\mathrm{T}^{2})$ Gravity

Abstract: The main purpose of this paper is to obtain physically stable stellar models coupled with anisotropic matter distribution in the context of $f(\mathcal{R},\mathrm{T}^{2})$ theory. For this, we consider a static spherical geometry and formulate modified field equations containing various unknowns such as matter determinants and metric potentials. We then obtain a unique solution to these equations by employing Durgapal-Fuloria ansatz possessing a constant doublet. We also use matching criteria to calculate the values of these constants by considering the Schwarzschild exterior spacetime. Two different viable models of this modified theory are adopted to analyze the behavior of effective matter variables, anisotropy, energy conditions, compactness and redshift in the interiors of Her X-1, PSR J0348-0432, LMC X-4, SMC X-1, Cen X-3, and SAX J 1808.4-3658 star candidates. We also check the stability of these models by using three different physical tests. It is concluded that our considered stars satisfy all the physical requirements and are stable in this modified gravity for the considered parametric values.