Effects of light-mass fermionic dark matter on the equilibrium and stability of white dwarfs

White dwarfs (WDs) can be used as laboratories to test strong gravity and high-density regimes, once their equation of state is not so uncertain as the one of neutron stars. This makes them also a useful tool to constrain dark-matter models. In this work, we study dark matter white dwarfs (DMWD) composed of white dwarf matter admixed with fermionic dark matter in a two-fluid general relativistic framework. Dark matter particles are considered to have masses between 0.1--10 GeV. The equilibrium configurations and stability are derived, showing that the DMWD can be more compact, with masses around $1.3M\ensuremath{\bigodot}$ and radii around 500 km. The increasing compactness leads to changes in the fundamental modes of radial oscillations ($\ensuremath{\sim}20%$ for 0.1 GeV DM), which produce detectable shifts in GW frequencies. The interplay between dark matter and normal matter thus provides a compelling avenue for interpreting deviations in observed WD properties and for placing constraints on DM characteristics through astrophysical observations.