On an alternative mechanism for the black hole echoes

TL;DR

This paper proposes an alternative mechanism for black hole echoes based on a discontinuity in the black hole metric, supported by numerical and analytical analysis, with implications for understanding quantum gravity and astrophysical observations.

Contribution

It introduces a novel mechanism for black hole echoes involving metric discontinuities, expanding the theoretical framework and providing analytical and numerical evidence.

Findings

Echoes persist even with distant and weak discontinuities.

The period of echoes relates to the pole spacing in quasinormal modes.

Discontinuities modify the asymptotic behavior of quasinormal frequencies.

Abstract

Gravitational wave echoes from the black holes have been suggested as a crucial observable to probe the spacetime in the vicinity of the horizon. In particular, it was speculated that the echoes are closely connected with specific characteristics of the exotic compact objects, and moreover, possibly provide an access to the quantum nature of gravity. Recently, it was shown that the discontinuity in the black hole metric substantially modifies the asymptotical behavior of quasinormal frequencies. In the present study, we proceed further and argue that a discontinuity planted into the metric furnishes an alternative mechanism for the black hole echoes. Physically, the latter may correspond to an uneven matter distribution inside the surrounding halo. To demonstrate the results, we first numerically investigate the temporal evolution of the scalar perturbations around a black hole that possesses a nonsmooth effective potential. It is shown that the phenomenon persists even though the discontinuity can be located further away from the horizon with rather insignificant strength. Besides, we show that the echoes in the present model can be derived analytically based on the modified pole structure of the associated Green function. The asymptotical properties of the quasinormal mode spectrum and the echoes are found to be closely connected, as both features can be attributed to the same origin. In particular, the period of the echoes in the time domain $T$ is shown to be related to the asymptotic spacing between successive poles along the real axis in the frequency domain $\Delta(\Re\omega)$, by a simple relation $\lim\limits_{\Re\omega\to+\infty}\Delta(\Re\omega) = 2\pi/T$. Moreover, we discuss possible distinguishment between different echo mechanisms. The potential astrophysical implications of the present findings are also addressed.