Probing the Dense Matter Equation of State through Neutron Star Oscillations and Gravitational Waves

Neutron stars, with their extreme densities and strong gravitational fields, provide a natural laboratory to explore the physics of dense matter and the equation of state (EOS) that governs it. Probing the EOS through neutron star oscillations—manifested as quasi-normal modes (QNMs)—offers a unique opportunity to extract information about the internal structure and composition of these compact objects. In this poster, I will introduce how oscillation modes, such as g-modes and f-modes, are influenced by different EOSs, including those incorporating phase transitions or dark matter. Low-frequency modes such as g-modes can be resonantly excited in merging neutron stars through dynamical tides. By examining the characteristic frequencies and damping times of these oscillations, we identify observable signatures that may be detected through gravitational waves or electromagnetic observations.