On an alternative mechanism for the black hole echoes

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. Moreover, 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 ∆( ω), by a simple relation lim ω→+∞ ∆( ω) = 2π/T . The potential astrophysical implications of the present findings are addressed.

Matrix method for perturbed black hole metric with discontinuity

“…Apart from the quasinormal mode structural instability, discontinuity in the metric is known for other interesting implications. It was shown that discontinuity in the effective potential furnishes a possible origin of black hole echoes [65], which was understood as due to the modification to the pole structure of Green's function. The presence of a dusty thin shell was found to affect the black hole shadow non-trivially [66].…”

Ellis drainhole solution in Einstein-Æther gravity and the axial gravitational quasinormal modes

“…The numerically extracted quasinormal frequencies are consistent with those obtained by the WKB and other methods, while the late-time tail follows a power-law, the exponent is different from that of the Schwarzchild black hole. More recently, the gravitational wave echoes [33][34][35] were also explored in terms of dissipative oscillations in wormholes [36,37]. Following this line of thought, in the present study, we derive an Ellis drainhole solution [16,17] in the Einstein-AEther gravity and explore the axial gravitational quasinormal modes.…”

Cuspy and fractured black hole shadows in a toy model with axisymmetry

“…In fact, discontinuity is present at the surface of compact celestial objects, and the numerical calculations of the curvature modes have indeed confirmed such a nontrivial consequence [59]. Furthermore, it was recently speculated that discontinuity due to a thin disk of matter provides an alternative mechanism of the echo phenomenon [60]. Considering that the quasinormal frequencies at the eikonal limit are closely connected with the shadow and photon sphere in spherical metrics [21,61], it is natural to ask whether some discontinuity out of the horizon of the black hole might lead to meaningful implications in the context of the black hole shadow.…”