Constructing stellar solutions with spherical symmetry through quadratic anisotropy in f(Q) gravity

Abstract This article examines anisotropic models to characterize compact stars (CSs) in the context of modified f(Q) gravity theory. To achieve this, we employ the linear functional form $$f(Q) = \alpha Q + \beta $$ f ( Q ) = α Q + β . A physically meaningful metric potential $$g_{rr}$$ g rr is considered, and a quadratic form of anisotropy is utilized to solve the Einstein field equations in closed form. This class of solutions is then applied to characterize observed pulsars from various perspectives. In the scope of f(Q) gravity, we address the Darmois–Israel junction requirements to guarantee a smooth matching of the inner metric with the external metric (Schwarzschild (Anti-) de Sitter solution) at the boundary hypersurface. By applying these junction conditions, we determine the model parameters involved in the solutions. Additionally, this study evaluates the physical viability and dynamical stability of the solution for different values of the f(Q)-parameter $$\alpha $$ α within the compact star (CS). The mass–radius relationships associated with observational constraints are analyzed for several compact stars, including Vela X-1, PSR J1614-2230, and PSR J0952-0607. The investigation indicates that the estimated radius of the compact object PSR J0952-0607, with mass $$2.35 \pm 0.17~M_\odot $$ 2.35 ± 0.17 M ⊙ , is around $$15.79^{+0.05}_{-0.09}$$ 15 . 79 - 0.09 + 0.05 km for a particular parameter value of $$\alpha = 2.0$$ α = 2.0 , and the moment of inertia for the de Sitter space is determined as $$4.31 \times 10^{45}~\textrm{g}~\textrm{cm}^2$$ 4.31 × 10 45 g cm 2 . The $$I-M$$ I - M curve shows greater sensitivity to the stiffness of the equation of state than the $$M-R$$ M - R curve, reinforcing our conclusion about the $$I-M$$ I - M framework’s responsiveness. Finally, we predicted the corresponding radii and moments of inertia for various values of $$\alpha $$ α based on the $$M-R$$ M - R and $$M-I$$ M - I curves.