Radial and non-radial oscillations of protoneutron stars with hyperonic composition

This paper studies radial and non-radial oscillations of protoneutron stars (PNSs) evolving from hot, neutrino-rich states to cold, catalyzed configurations, using a density-dependent relativistic mean-field equation of state (EoS) with nucleonic and hyperonic matter. The fundamental ( f ) and first pressure ( p₁ p 1 ) modes are computed in both the Cowling approximation and full general relativity (GR). For the f -mode, the Cowling approximation overestimates the frequency by ~ 24% ∼ 24 % in the hot phase, increasing to ~ 28% ∼ 28 % at $$T=0$$ T = 0 for MB=1.5\,M_ M B = 1.5 M ⊙ , and by ~ 19% ∼ 19 % (hot/intermediate) rising to ~ 22% ∼ 22 % at $$T=0$$ T = 0 for MB=2.3\,M_ M B = 2.3 M ⊙ . For the p₁ p 1 -mode, deviations are smaller: ~ 6.7% ∼ 6.7 % (hot), peaking at ~ 10% ∼ 10 % during deleptonization, and decreasing to ~ 6.6% ∼ 6.6 % at $$T=0$$ T = 0 . Hyperons slightly increase oscillation frequencies. Stage-dependent f -mode scaling shows that expressing <jats:inline-formula