# Echoes from Quantum Black Holes

## TL;DR

This paper investigates gravitational wave echoes from quantum black holes with a universal Boltzmann reflectivity, deriving their quasi-normal modes, analyzing their decay patterns, and predicting their detectability in future observations.

## Contribution

It analytically derives quasi-normal modes for quantum black holes with Boltzmann reflectivity and compares predictions with numerical simulations, advancing understanding of potential quantum gravity signatures in gravitational waves.

## Key findings

- Echo amplitudes decay inversely with time initially
- Subsequent echoes decay exponentially
- Echo signals could be detectable for massive spinning black holes

## Abstract

One of the most triumphant predictions of the theory if general relativity was the recent LIGO-Virgo detection of gravitational wave (GW) signals produced in binary black hole (BH) mergers. However, it is suggested that exotic compact objects, proposed in quantum gravity models of BHs, may produce similar classical GW waveforms, followed by delayed repeating "echoes". In a companion paper [1], we have presented different arguments for a universal Boltzmann reflectivity of quantum BH horizons. Here, we investigate the resulting echoes from this prescription. We derive corresponding quasi-normal modes (QNMs) for quantum BHs analytically, and show how their initial conditions can be related to the QNMs of classical BHs. Ergoregion instability is suppressed by the imperfect reflectivity. We then compare the analytic and numerical predictions for echoes in real time, verifying their consistency. In particular, we find that the amplitudes of the first ~20 echoes decay inversely with time, while the subsequent echoes decay exponentially. Finally, we present predictions for the signal-to-noise ratio of echoes for spinning BHs, which should be imminently detectable for massive remnants, subject to the uncertainty in the nonlinear initial conditions of the BH merger.