Non-radial oscillations and gravitational wave radiation of proto-neutron stars

We study the g-mode non-radial oscillations of proto-neutron stars during the cooling stage. Based on finite-temperature extended Brueckner–Hartree–Fock theory and the relativistic mean-field theory, and combined with appropriate crust equations of state, we construct isentropic equations of state for proto-neutron stars with neutrino trapping. Under the frozen-fluid assumption during oscillations, the difference between the adiabatic and equilibrium sound speeds gives rise to nonzero Brunt–Väisälä frequencies, which enables the existence of g-mode oscillations. We then study the effects of temperature and neutrino trapping on the g-mode frequencies under the Cowling approximation, making comparisons between results with the two EOSs and examining the impact of varying crust equations of state. Our results show that, compared with cold neutron stars, neutrino trapping significantly reduces gravity-mode frequencies in both models, and the relativistic mean-field model systematically yields lower frequencies than the Brueckner–Hartree–Fock model. Neutrino trapping also prolongs gravitational wave damping times and reduces the strain amplitudes, but predictions indicate that the signals remain within the sensitivity of current and future detectors. These findings highlight the potential of gravitational wave observations to probe the interior physics of proto-neutron stars.