$f$-Mode oscillations and the gravitational response of compact stars with analytic equations of state

We use a simple holographic model to study the property of cold and dense neutron stars (NSs) and deconfined QCD matter. With the aim of investigating the global properties of compact stars, such as the total gravitational mass and radius, the equation of states (EOS) of neutron stars and quark stars (QSs) are used to solve the Tolman-Oppenheimer-Volkov (TOV) equations for stellar structure. Additionally, we investigate the tidal deformabilities and $f$-mode oscillation for these two different compact stars. Our main conclusion is that, by using a holographic equation of state, it is possible to obtain neutron matter and quark matter properties and that it is also possible to extend the procedure to astrophysical applications.