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

Abstract 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 ( $$p_1$$ 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 $$\sim 24\%$$ ∼ 24 % in the hot phase, increasing to $$\sim 28\%$$ ∼ 28 % at $$T=0$$ T = 0 for $$M_B=1.5\,M_\odot $$ M B = 1.5 M ⊙ , and by $$\sim 19\%$$ ∼ 19 % (hot/intermediate) rising to $$\sim 22\%$$ ∼ 22 % at $$T=0$$ T = 0 for $$M_B=2.3\,M_\odot $$ M B = 2.3 M ⊙ . For the $$p_1$$ p 1 -mode, deviations are smaller: $$\sim 6.7\%$$ ∼ 6.7 % (hot), peaking at $$\sim 10\%$$ ∼ 10 % during deleptonization, and decreasing to $$\sim 6.6\%$$ ∼ 6.6 % at $$T=0$$ T = 0 . Hyperons slightly increase oscillation frequencies. Stage-dependent f -mode scaling shows that expressing