Neutrino Fluence influenced by Memory Burdened Primordial Black Holes

We study the impact of quantum gravitational memory burden - a backreaction effect that suppresses black hole evaporation - on neutrino signals from primordial black holes (PBHs). This suppression, modeled via a parameter k, reduces the high-energy muon neutrino fluence, particularly during the late stages of evaporation. We also consider beyond the Standard Model scenarios in which heavy neutral leptons (HNLs) are emitted by PBHs and subsequently decay, injecting secondary neutrinos that partially mitigate the suppression in the MeV-GeV range. We compute the full time-integrated neutrino spectrum and evaluate the expected IceCube event rates across the (k, mN) parameter space. We analyze both single source burst scenarios and the cumulative Galactic contribution assuming PBHs trace a realistic dark matter halo distribution. Even under optimistic proximity assumptions, the predicted event rates remain far below IceCube sensitivity, and population-level stacking within current observational bounds on the PBH abundance does not yield an observable signal in the considered mass range for PBH abundances consistent with existing observational constraints. These results demonstrate that entropy-suppressed evaporation substantially weakens neutrino detectability of light PBHs and must be consistently incorporated in future multi-messenger searches.