$g$-mode oscillations of dark matter admixed neutron stars

We investigate $g$-mode oscillations in dark matter admixed neutron stars employing a relativistic mean field model to describe hadronic matter and a model for self-interacting fermionic dark matter motivated by the neutron decay anomaly. Following the construction of such admixed configurations, we derive the equilibrium and adiabatic speeds of sound therein, leading to a computation of the star's $g$-mode spectrum in the Cowling approximation. In particular, we explore the effect of dark matter self-interaction, the nucleon effective mass and dark matter fraction on the principal $g$-mode frequency, and its first overtone. We show that the effect on $g$-mode frequency depends predominantly on the dark matter fraction, and demonstrate an equation of state-independent constraint for the latter. Prospects of identifying the presence of dark matter in neutron stars using $g$-mode are discussed.