Echoes from corpuscular black holes

Abstract: In the corpuscular picture of black hole there exists no geometric notion of horizon which, instead, only emerges in the semi-classical limit. Therefore, it is very natural to ask - what happens if we send a signal towards a corpuscular black hole? We show that quantum effects at the horizon scale imply the existence of a surface located at an effective radius $R=R_s(1+\epsilon)$ slightly larger than the Schwarzschild radius $R_s,$ where $\epsilon=1/N$ and $N$ is the number of gravitons composing the system. Consequently, the reflectivity of the object can be non-zero and, indeed, we find that incoming waves with energies comparable to the Hawking temperature can have a probability of backscattering of order one. Thus, modes can be trapped between the two potential barriers located at the photon sphere and at the surface of a corpuscular black hole, and periodic echoes can be produced. The time delay of echoes turns out to be of the same order of the scrambling time, i.e., in units of Planck length it reads $\sqrt{N}\,{\rm log}\,N.$ We also show that the $\epsilon$-parameter, or in other words the compactness, of a corpuscular black hole coincides with the quantum coupling that measures the interaction strength among gravitons, and discuss the physical implications of this remarkable feature.