Black Holes as Catalysts for Cosmic String Detection and Axion Dark Matter Genesis

The global $U_{PQ}(1)$ Peccei-Quinn (PQ) symmetry, proposed to resolve the strong CP problem, predicts the existence of the axion, a pseudo Nambu-Goldstone boson and a leading dark matter candidate. The spontaneous breaking of this symmetry generates global strings that decay predominantly via the emission of massive axions and gravitational waves. In this work, we investigate the decay of cosmic axion strings in the vicinity of a Schwarzschild black hole and estimate the corresponding energy losses and decay timescales of the resulting string loops. For primordial black holes (PBHs) with masses as small as $10^{-16} M_\odot$, the total radiated energy by the string is found to be on the order of $10^{27}$ GeV, encompassing both axion emission and gravitational waves. A key finding is that the presence of a central black hole significantly accelerates the decay of cosmic string loops, substantially reducing their lifetimes. We present these results as an initial estimate of axion radiation from PBH-cosmic string systems along with the decay time as an important observational signature for axions strings.