Echoes from hairy black holes

A bstract We study the waveforms of time signals produced by scalar perturbations in static hairy black holes, which can be governed a double-peak effective potential. The inner potential peak would give rise to echoes, provide powerful tool test Kerr hypothesis. are constructed and frequency domains, we find that late-time determined long-lived sub-long-lived quasinormal modes, trapped valley near smaller peak, respectively. When distance between peaks is significantly larger than width peaks, train decaying echo pulses superposition modes. In certain cases, echoes vanish then reappear. close enough, one detects far fewer following sinusoid tail, controlled or mode hence decays very slowly.