Exploring the physical properties of anisotropic compact objects and constraining their mass–radius relations beyond standard limit in F(Q)-gravity

The progress in theoretical modeling of compact high-mass stars in the context of alternative gravity has become important in minimizing challenges associated with neutron star (NS) radius measurements. On this basis, we have presented a rigorous study of compact objects beyond the standard limit in gravity $F\left(Q\right)$ in particular $F\left(Q\right)=b_{1}Q+b_2$ where $b_1$ and $b_2$ are constants. After formulating the basic equations and finding their relevant solutions by assuming a well-behaved ansatz for the metric potential as well as for anisotropy monitored by the parameters ${\mu }_1,{\mu }_2,b_1$, along with imposing the boundary conditions on the system under treatment, we have developed a stellar model for anisotropic stars. Specifically, we explored the physical properties of these anisotropic stars and provided novel mass–radius ($M-R$) relations with models falling in the mass gap of the events GW190814 and GW200210, as well as the effects of slow rotation and moment of inertia on these findings. Interestingly, the behavior of the $M-R$ curves represents a polytropic-type equation of state (EOS) for a negative $\Lambda$, while a positive $\Lambda$ corresponds to a quark matter EOS. However, the analysis reveals that the predicted radii of the compact object observed in the GW190814 event, with a mass of 2.5–2.67 $M_{\odot }$, is approximately 11.4 km for the de Sitter (dS) case and 11.8 km for the anti-de Sitter (AdS) case, assuming a specific value of the parameter $b_1=1.1$. Furthermore, for $b_1>1.1$, the model predicts the existence of more compact stars with a maximum mass of approximately $3M_{\odot }$, which is in good agreement with the $R^2$ model of NSs maintaining the Sly EOS. From the $I-M$ curves, it can be observed that higher values of $b_1$ and ${\mu }_1$ in $F\left(Q\right)$ gravity can sustain high moments of inertia (I) of stars with high masses. Interestingly, we obtained the range of $I$ for the dS space as [$1.92,3.92$]$\times 10^{45}{\mathrm{gcm}}^2$ and for the AdS space as [$2.01,4.03$]$\times 10^{45}{\mathrm{gcm}}^2$ for $1.0\le b_1\le 1.2$.