Could the KM3–230213A event be caused by an evaporating primordial black hole?

We investigate whether the ultrahigh energy neutrino inferred by the recent KM3NeT observation could have originated from an evaporating black hole. Given the characteristics of the black hole evaporation mechanism, any object capable of producing particles in the energy range of the detected event (∼100-800  PeV) must have a mass MBH≲10⁷ g. No known astrophysical mechanism can generate black holes of such low mass, leaving primordial black holes (PBHs) - potentially formed at the end of cosmic inflation - as the only viable candidates. Black holes with masses MBH≲10⁷ g have lifetimes shorter than 10⁻⁵ seconds, meaning PBHs in this mass range should have fully evaporated by now. However, recent studies suggest that quantum effects, collectively referred to as the "memory burden," may slow down black hole evaporation, potentially extending the lifetimes of low-mass PBHs to timescales comparable to or exceeding the Hubble time. We systematically explore the parameter space of memory-burdened PBHs, assuming that they constitute a fraction of the dark matter (fPBH) within current constraints, and identify viable regions that could explain the KM3-230213A event. We further predict the occurrence rate of similar events, and find that KM3NeT and future neutrino experiments could test this scenario over the next years.