Unveiling the Equation of State Through Gravitational Wave Observations Involving Neutron Stars

Neutron star mergers are among the most violent collisions in the universe, offering a unique window into the equation of state of dense matter. The gravitational waves emitted during these mergers encode information about the tidal interactions and masses of the neutron stars involved. These serve as powerful but indirect probes of the underlying nuclear physics governed by the equation of state. However, extracting precise equation of state constraints from these observations remains a significant challenge due to degeneracies arising from unknown particle compositions, uncertainties in the underlying physics, and the potential influence of dark matter. In this talk, I will focus on recent methods developed to extract the most precise equation of state constraints from existing gravitational wave observations. I will also highlight how observations using next-generation, highly sensitive gravitational wave detectors are expected to further enhance our ability to probe the nature of nuclear matter at extreme densities.