Xin-Chen He, Xiao-Han Ma, Misao Sasaki, Volodymyr Takhistov

Evaporating black holes can leave distinct imprints on gravitational wave (GW) backgrounds. We show that black hole populations with finite width mass distributions exhibit a universal late time evolution governed by the evaporation dynamics rather than the details of the initial mass distribution, leading to a characteristic power law suppression of the induced GWs. We demonstrate this for a broad class of mass functions in primordial black hole (PBH) scenarios featuring an early Universe matter-dominated era, and identify the suppression of PBH-induced GWs found for critical collapse distributions as a manifestation of this general phenomenon. Our results establish a direct connection between the asymptotic GW spectrum and the underlying law of black hole evaporation.