Radial Oscillations and Stability of Neutron Stars with Antikaon Condensates

Abstract: Radial oscillations provide a direct probe of the stability and compressibility of neutron stars and are highly sensitive to the equation of state of dense matter. In this work, we investigate the impact of antikaon condensates on the radial oscillation properties of neutron stars. For this purpose, we model neutron star matter using equations of state with a wide range of stiffness. Both non--linear and density--dependent relativistic mean--field frameworks are employed to develop equations of state that are consistent with current astrophysical constraints. We further consider the emergence of antikaon condensates ($K^-$ and $\bar{K}^0$) in the stellar core, which modifies the pressure--energy density relation of dense matter. We find that the nature of the transition from nuclear matter to the condensed phase is sensitive to the antikaon optical potential depth. We compute the fundamental and higher--order radial oscillation modes for neutron stars containing antikaon condensates over a range of antikaon optical potential depths. Our results demonstrate that the antikaon optical potential depth plays a decisive role in governing the systematic shifts observed in the radial oscillation frequencies, while also significantly reducing the stability limits and maximum masses of neutron stars. These imprints of antikaon condensation on radial oscillation spectra provide a promising avenue for future multi--messenger observations and high--frequency gravitational--wave searches to directly probe and constrain the internal composition and equation of state of neutron stars.