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In many well-motivated new physics models, the pseudo-Nambu-Goldstone boson(pNGB) from U(1) symmetry breaking emerges as a promising dark mattercandidate. Its coupling, suppressed by the symmetry breaking scale, preventsthermal equilibrium in the early Universe for high scale symmetry breaking.Thus, pNGB dark matter is predominantly produced via non-thermal mechanisms,such as the freeze-in process through a new portal coupling. In this work, weexplore a novel mechanism for the production of pNGB dark matter even withfeeble Higgs portal coupling-arising from Hawking radiation or superradiance ofprimordial black holes. We systematically investigate the production of lightand heavy pNGB dark matter, both for Schwarzschild and Kerr black holes. Wealso discuss its potential gravitational wave signatures from domain wallcollapse, density perturbations, and Hawking radiation. If the ultraviolet (UV)model is considered, the recent $\mathcal{O}$(100) PeV neutrino eventKM3-230213A at KM3NeT can be naturally explained.

Pseudo-Goldstone Dark Matter from Primordial Black Holes: Gravitational Wave Signatures and Implications for KM3-230213A Event at KM3NeT