Echoes from Hairy Black Holes

TL;DR

This paper investigates scalar wave echoes in hairy black holes with double-peak potentials, revealing how quasinormal modes influence late-time signals and the conditions under which echoes appear or vanish.

Contribution

It introduces a detailed analysis of waveforms in hairy black holes with double-peak potentials, highlighting the role of quasinormal modes in echo formation and decay.

Findings

Echoes depend on the distance between potential peaks.

Long-lived modes trap energy, producing persistent echoes.

Close peaks suppress echoes, leading to slow-decaying tails.

Abstract

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