Oscillation frequencies excited in neutron stars are crucial for extracting their interior properties. In addition to the fundamental and pressure modes, the gravity ($g$-)modes can be excited even in zero-temperature stellar models due to the composition gradient. In this study, we systematically study the $g$-mode frequencies, focusing on the nucleonic equation of state. Then, we derive an empirical relation for the first $g$-mode frequencies as a function of the stellar compactness and the combination of the nuclear saturation parameters, ${\eta }_0\equiv L/K_0$, where $K_0$ and $L$ denote the incompressibility of symmetric nuclear matter and the density dependence of the nuclear symmetry energy, respectively. If an observed first $g$-mode frequency significantly deviates from our empirical relation, it may indicate the emergence of additional degrees of freedom or new compositions inside the star.

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• Equations of state
• Gravitational waves
• Nuclear matter in neutron stars
• Neutron stars & pulsars