Exploring the universal $\bar{\mathcal{I}}-\mathcal{C}$ relations for relativistic stars in $f(Q)$ gravity

We investigate the properties of neutron stars within the framework of $f(Q)$ gravity by incorporating rotational effects through a slowly rotating metric. We derive the modified TOV equations and calculate the angular velocity profiles and moments of inertia (MOI) for linear, quadratic, exponential, and logarithmic $f(Q)$ models. Our results show that deviations in the MOI are more pronounced than those in the stellar mass profiles, suggesting that rotational observables are highly sensitive to geometric corrections. We also calculate a quasi-universal relation between the dimensionless MOI and compactness ($\bar{I}$-$C$). The linear and quadratic models are generally consistent with observational data from PSR J0737-3039A, although the deviations are small and difficult to distinguish from General Relativity due to inherent EoS variability. On other hand, the logarithmic and exponential models show larger deviations (over 20 %), exceeding the EoS-induced uncertainty reported by Suleiman & Read (2024), highlighting the relation's sensitivity to the $f(Q)$ gravity model. These results indicate that $f(Q)$ gravity could potentially be tested in the strong-field regime and point to a direction for future studies, such as investigating EoS-insensitive quasi-universal relations, like the $\bar{I}(\Lambda)$ relations, within the $f(Q)$ framework. Such relations may provide a clearer pathway for exploring possible signatures in strong-field gravity when combined with more precise future observations.