Black Hole Echoes Overview

• Black hole echoes are repeated, delayed signals observed after gravitational-wave events, generated by trapping between near-horizon reflectors and angular momentum barriers.
• They arise from diverse mechanisms including quantum modifications, classical discontinuities, and optical caustics, each providing distinct time-domain signatures.
• Studies leverage both quantum and classical models to explore echo phenomena, offering insights into black-hole structure, modified gravity, and astrophysical processes.

Black hole echoes are delayed, repeated responses associated with signal propagation in black-hole spacetimes or black-hole analogues. In the dominant gravitational-wave usage, they are late-time post-merger pulses generated when the usual outer angular-momentum barrier is supplemented by a partially reflecting structure near the horizon or by an additional exterior barrier. The same term is also used for classical caustic repetitions in the Schwarzschild Green function, for strong-lensing light echoes, for optical echo tails in analogue-gravity models, and for stochastic correlation signals in black-hole phase transitions. The literature is therefore heterogeneous: “echo” denotes a family of delayed-return phenomena rather than a single mechanism (Abedi et al., 2016, Zenginoğlu et al., 2012, Liu et al., 2021, Wong et al., 2024, Yue et al., 27 Oct 2025).

1. Terminology and scope

In gravitational-wave phenomenology, a black hole echo is usually a train of delayed, damped pulses following the prompt ringdown, produced by repeated partial trapping between two scattering structures. In that canonical usage, the inner structure is placed very close to the would-be horizon, while the outer structure is the standard light-ring or angular-momentum barrier (Abedi et al., 2016). By contrast, classical field-theory and lensing papers use the same term for repeated arrivals generated by photon-sphere trapping, caustics, multi-path null geodesics, or kinetic correlations, without any horizon-scale reflector (Zenginoğlu et al., 2012, Wong et al., 2024, Yue et al., 27 Oct 2025).

A second distinction is interpretive. Some papers treat echoes as possible probes of Planck-scale horizon structure, area quantization, fuzzballs, firewalls, or other quantum modifications. Others show that qualitatively similar delayed repetitions can arise in entirely classical settings: nonsmooth effective potentials, double-peaked barriers, hairy black holes, wormholes, or large-scale modified-gravity backgrounds (Cardoso et al., 2019, Liu et al., 2021, Huang et al., 2021, Guo et al., 2022, Momennia, 6 Feb 2025).

Usage	Mechanism	Representative papers
Gravitational-wave ringdown echoes	Cavity between angular-momentum barrier and near-horizon reflector	(Abedi et al., 2016, Burgess et al., 2018)
Environmental or classical cavity echoes	Discontinuity or double-peaked exterior effective potential	(Liu et al., 2021, Huang et al., 2021, Guo et al., 2022)
Caustic echoes	Photon-sphere trapping and caustic passage in Schwarzschild	(Zenginoğlu et al., 2012)
Light echoes	Multiple lensed null geodesics and delayed subimages	(Wong et al., 2024)
Optical echo tails	Photon-sphere resonance in an analogue-gravity Flamm paraboloid	(Ju et al., 5 Jan 2026)
Stochastic kinetic echoes	Correlation difference in RNAdS phase-switching statistics	(Yue et al., 27 Oct 2025)

2. Near-horizon gravitational-wave echoes

The canonical echo paradigm modifies the classical black-hole boundary condition. In classical general relativity, the ringdown problem is posed with waves purely outgoing at infinity and purely ingoing at the horizon, so there is no repeated late-time return. Echoes appear when the horizon is replaced, effectively, by a partially reflective structure just outside $r_+$, so that inward-going radiation can bounce between that structure and the exterior barrier (Abedi et al., 2016). For a membrane placed a Planck proper length outside the horizon, the inter-echo delay scales logarithmically with the microscopic offset and, in the Schwarzschild estimate highlighted in the early echo literature, takes the form

$\Delta t_{\rm echo}=8M\log(M/l_p)$

with spin corrections (Abedi et al., 2016).

An effective-field-theory treatment replaces microscopic near-horizon physics by a boundary action on a stretched horizon and shows that low-energy dynamics are dominated by linear Robin boundary conditions rather than arbitrary hard-wall prescriptions (Burgess et al., 2018). In that language the observable transfer function is

$$\mathcal{K}=\frac{\mathcal{T}_{\rm BH}\mathcal{R}}{1-\mathcal{R}_{\rm BH}\mathcal{R}},$$

where $\mathcal{R}$ is the near-horizon reflection amplitude and $\mathcal{R}_{\rm BH},\mathcal{T}_{\rm BH}$ are the standard barrier reflection and transmission factors (Burgess et al., 2018). The same analysis identifies the perfect absorber and perfect emitter as the only RG fixed points; the classical GR horizon corresponds to the absorber fixed point (Burgess et al., 2018).

Several papers then specify microscopic reflectivity laws. In the Bekenstein-Mukhanov area-quantization scenario, the horizon absorbs only at discrete frequencies

$\omega_n=\frac{n\alpha}{32\pi M},$

so the near-horizon surface becomes a frequency-selective filter rather than a broadband absorber (Cardoso et al., 2019). The prompt ringdown remains approximately classical, while later echoes are spectrally sculpted because the $k$-th echo is multiplied by $R^k(\omega)$ (Cardoso et al., 2019). In the “Boltzmann echoes” framework, the reflected-to-incident energy ratio is

$$\frac{E_{\rm out}}{E_{\rm in}}=\exp\!\left(-\frac{\hbar |\tilde{\omega}|}{k_B T_{\rm H}}\right),$$

with $\tilde{\omega}=\omega-m\Omega_H$; the corresponding time-domain analysis predicts that the amplitudes of the first $\Delta t_{\rm echo}=8M\log(M/l_p)$0 echoes decay inversely with time, while later echoes decay exponentially, and that imperfect reflectivity suppresses the ergoregion instability (Wang et al., 2019).

Other near-horizon models alter not only the modulus but also the channel structure of reflection. “New Kind of Echo from Quantum Black Holes” proposes a two-component Andreev-reflector boundary condition in which an incoming mode produces both a normally reflected particle-like component and a hole-like component with a characteristic relative phase (Manikandan et al., 2021). The same paper argues that every other echo can be enhanced by repeated Andreev conversion and that this phase structure may encode a near-horizon quantum state (Manikandan et al., 2021). In the corpuscular or $\Delta t_{\rm echo}=8M\log(M/l_p)$1-portrait picture, finite $\Delta t_{\rm echo}=8M\log(M/l_p)$2 replaces the exact horizon by an effective surface at

$\Delta t_{\rm echo}=8M\log(M/l_p)$3

with $\Delta t_{\rm echo}=8M\log(M/l_p)$4 equal to the graviton coupling $\Delta t_{\rm echo}=8M\log(M/l_p)$5; for modes with $\Delta t_{\rm echo}=8M\log(M/l_p)$6, the reflectivity can be order unity, and the echo delay becomes

$\Delta t_{\rm echo}=8M\log(M/l_p)$7

of the same order as the scrambling time (Buoninfante, 2020).

3. Classical and environmental echo mechanisms

A major development after the first quantum-horizon echo proposals was the demonstration that delayed ringdown-like repetitions are not unique to exotic near-horizon structure. “On an alternative mechanism for the black hole echoes” shows that a discontinuity or nonsmooth feature implanted in the metric, equivalently in the effective potential, can generate echoes even when it is weak and far outside the horizon (Liu et al., 2021). In the simplest model, a Regge-Wheeler potential truncated at $\Delta t_{\rm echo}=8M\log(M/l_p)$8 creates partial reflection at the discontinuity, so the echo cavity is formed by the ordinary black-hole potential peak on one side and a distant discontinuity on the other (Liu et al., 2021). The paper further derives the spectral-time relation

$\Delta t_{\rm echo}=8M\log(M/l_p)$9

linking the asymptotic spacing of the extra pole family to the echo period $$\mathcal{K}=\frac{\mathcal{T}_{\rm BH}\mathcal{R}}{1-\mathcal{R}_{\rm BH}\mathcal{R}},$$0 (Liu et al., 2021).

Entirely classical black holes can also echo if their perturbation potentials develop two separated barriers. In Einstein-Maxwell gravity with a quasi-topological electromagnetic term, dyonic black holes satisfying the dominant energy condition can exhibit a double-peaked scalar effective potential, and a wave packet trapped between the two peaks yields a late-time echo train even though the spacetime has a genuine event horizon and standard ingoing boundary conditions at the horizon (Huang et al., 2021). For initial data released inside the cavity, the paper reports that the echo frequency is about twice that of a packet released outside (Huang et al., 2021).

A related mechanism appears in static hairy black holes in Einstein-Maxwell-scalar theory. There the inner peak of a double-peak scalar potential acts as an effective reflector, the valley between the peaks supports long-lived modes, and the late-time signal is controlled by long-lived modes trapped in the valley and sub-long-lived modes localized near the smaller peak (Guo et al., 2022). When the peaks are well separated, the waveform becomes a train of decaying echo pulses; when they are close, only a few echoes remain and the late signal becomes a slowly decaying sinusoidal tail (Guo et al., 2022).

Modified gravity can shift the second barrier to much larger radius. In conformal Weyl gravity, a massive scalar perturbation sees an effective potential whose first peak is the usual black-hole barrier and whose second peak is generated by the large-scale linear $$\mathcal{K}=\frac{\mathcal{T}_{\rm BH}\mathcal{R}}{1-\mathcal{R}_{\rm BH}\mathcal{R}},$$1 term together with the cosmological constant (Momennia, 6 Feb 2025). The echo-producing conditions are

$$\mathcal{K}=\frac{\mathcal{T}_{\rm BH}\mathcal{R}}{1-\mathcal{R}_{\rm BH}\mathcal{R}},$$2

with the potential returning to zero at the cosmological horizon (Momennia, 6 Feb 2025). The corresponding echoes are therefore generated by the large-scale structure of the spacetime rather than by near-horizon modifications (Momennia, 6 Feb 2025).

The same general lesson appears in other settings. In novel black-bounce spacetimes, echoes are present only in the two-way traversable wormhole regime $$\mathcal{K}=\frac{\mathcal{T}_{\rm BH}\mathcal{R}}{1-\mathcal{R}_{\rm BH}\mathcal{R}},$$3, where the effective potential develops a well between barriers; they are absent in the regular-black-hole regime $$\mathcal{K}=\frac{\mathcal{T}_{\rm BH}\mathcal{R}}{1-\mathcal{R}_{\rm BH}\mathcal{R}},$$4 and in the one-way wormhole case $$\mathcal{K}=\frac{\mathcal{T}_{\rm BH}\mathcal{R}}{1-\mathcal{R}_{\rm BH}\mathcal{R}},$$5 (Yang et al., 2021). In $$\mathcal{K}=\frac{\mathcal{T}_{\rm BH}\mathcal{R}}{1-\mathcal{R}_{\rm BH}\mathcal{R}},$$6 gravity, a merger can excite a rapidly oscillating, infalling Ricci scalar mode near the horizon, and the paper proposes that the resulting source-driven ringdown can mimic echo-like late-time structure without introducing an explicit reflective wall, although no explicit echo delay formula is derived (Sibandze et al., 2017). By contrast, a conservative Lorentz-violating EFT modification of the dispersion relation leaves the horizon only very weakly reflective, with $$\mathcal{K}=\frac{\mathcal{T}_{\rm BH}\mathcal{R}}{1-\mathcal{R}_{\rm BH}\mathcal{R}},$$7 scaling as $$\mathcal{K}=\frac{\mathcal{T}_{\rm BH}\mathcal{R}}{1-\mathcal{R}_{\rm BH}\mathcal{R}},$$8; the resulting echo power is correspondingly tiny, and strong echoes would require a more drastic departure from standard GR or EFT (D'Amico et al., 2019).

4. Caustic, optical, and stochastic echoes

The term “black hole echoes” also covers entirely classical retarded-propagator effects. “Caustic echoes from a Schwarzschild black hole” constructs the scalar Schwarzschild Green function in the time domain and shows that energy trapped near the photon sphere leaks out after repeated caustic passages, producing echoes that propagate to infinity (Zenginoğlu et al., 2012). The arrival intervals approach the null-geodesic orbital periods

$$\mathcal{K}=\frac{\mathcal{T}_{\rm BH}\mathcal{R}}{1-\mathcal{R}_{\rm BH}\mathcal{R}},$$9

and the fourfold singularity structure of the retarded Green function is traced to successive Hilbert transforms at caustics (Zenginoğlu et al., 2012). Because the echo train decays exponentially while the Price tail decays polynomially, only a finite number of echoes remain observable even with ideal instruments (Zenginoğlu et al., 2012).

In strong-lensing studies, a black hole light echo is a delayed subimage produced by photons that reach the observer along longer null geodesics. “Measuring Black Hole Light Echoes with Very Long Baseline Interferometry” defines subimages by time ordering, with the shortest-travel-time geodesic giving the direct image $\mathcal{R}$0 and higher-order geodesics giving $\mathcal{R}$1 (Wong et al., 2024). In M87-like GRMHD simulations, the characteristic delay between the direct and singly indirect image is of order $\mathcal{R}$2, and the higher-order images are demagnified, rotated, sheared, exponentially fainter copies concentrated in thin lensing bands near the critical curve (Wong et al., 2024). Because unresolved total light curves hide these weak delayed copies, the paper proposes correlating the total flux with long-baseline visibility amplitudes, which act as a proxy for indirect emission; in the simulations, baselines $\mathcal{R}$3 recover the expected delay (Wong et al., 2024).

A related analogue-gravity program studies optical echoes of pulsed light. In a Flamm-paraboloid model of Schwarzschild spatial geometry, a point-like Gaussian pulse emitted near the hole produces delayed optical echoes because successive geodesics acquire path-length increments approaching $\mathcal{R}$4 (Ju et al., 5 Jan 2026). The characteristic echo time and frequency are

$\mathcal{R}$5

and when the pulse length satisfies $\mathcal{R}$6, continuous “echo tails” appear along bright interference fringes (Ju et al., 5 Jan 2026). The paper interprets those tails as a resonance between the incoming pulse and the photon sphere (Ju et al., 5 Jan 2026).

A still more distant usage appears in black-hole thermodynamics. “Black hole echos reflect the phase transition and fluctuations in Hawking radiation” defines an echo not as a propagating wave pulse but as a two-event correlation signal in stochastic switching between small and large RNAdS black-hole phases (Yue et al., 27 Oct 2025). The diagnostic is

$\mathcal{R}$7

which vanishes if the two events are statistically independent (Yue et al., 27 Oct 2025). In that framework, the echo disappears when Hawking-rate fluctuation terms vanish, $\mathcal{R}$8, and also disappears when phase-transition kinetics vanish, $\mathcal{R}$9; the peak is largest near the free-energy degeneracy of the two phases (Yue et al., 27 Oct 2025).

5. Searches in gravitational-wave data

The first widely cited data analysis was “Echoes from the Abyss,” which searched the public O1 LIGO events GW150914, GW151226, and LVT151012 for repeating damped pulses with delays tied to the Kerr remnant parameters (Abedi et al., 2016). Using a phenomenological truncation-and-repeat template, that study reported tentative evidence with a false detection probability of $\mathcal{R}_{\rm BH},\mathcal{T}_{\rm BH}$0, corresponding to $\mathcal{R}_{\rm BH},\mathcal{T}_{\rm BH}$1, and in the combined analysis found $\mathcal{R}_{\rm BH},\mathcal{T}_{\rm BH}$2, $\mathcal{R}_{\rm BH},\mathcal{T}_{\rm BH}$3, and $\mathcal{R}_{\rm BH},\mathcal{T}_{\rm BH}$4 (Abedi et al., 2016). The paper was explicit that the template was ad hoc and that the result was not a discovery claim (Abedi et al., 2016).

The strongest individual claim in the early literature was made for GW170817. “Echoes from the Abyss: A highly spinning black hole remnant for the binary neutron star merger GW170817” used a model-agnostic cross-correlation search and reported a candidate at

$\mathcal{R}_{\rm BH},\mathcal{T}_{\rm BH}$5

around $\mathcal{R}_{\rm BH},\mathcal{T}_{\rm BH}$6 s after merger, with false alarm probability

$\mathcal{R}_{\rm BH},\mathcal{T}_{\rm BH}$7

and significance $\mathcal{R}_{\rm BH},\mathcal{T}_{\rm BH}$8 after look-elsewhere effects (Abedi et al., 2018). Interpreted as a quantum-horizon echo, the signal was consistent with a $\mathcal{R}_{\rm BH},\mathcal{T}_{\rm BH}$9 remnant and dimensionless spin $\omega_n=\frac{n\alpha}{32\pi M},$0 under the low-spin prior (Abedi et al., 2018).

The subsequent literature became explicitly contentious. “Echoes from the Abyss: A Status Update” argued that the various O1 and O2 searches could be mutually consistent if echoes are more prominent at lower frequencies and/or in binary mergers of more extreme mass ratio (Abedi et al., 2020). That paper further noted that the only reported $\omega_n=\frac{n\alpha}{32\pi M},$1 detection remained the GW170817 candidate and emphasized its temporal coincidence with the collapse time

$\omega_n=\frac{n\alpha}{32\pi M},$2

inferred from electromagnetic observations (Abedi et al., 2020). At the same time, it summarized a literature in which reported false alarm rates ranged broadly from $\omega_n=\frac{n\alpha}{32\pi M},$3 to $\omega_n=\frac{n\alpha}{32\pi M},$4, underscoring the sensitivity of significance estimates to waveform choice, prior volume, low-frequency treatment, and background estimation (Abedi et al., 2020).

A more recent targeted search focused on GW190521. “GW190521: Search for Echoes due to Stimulated Hawking Radiation from Black Holes” used both a template-based PyCBC analysis and an independent cWB reconstruction to test a stimulated-Hawking or Boltzmann-echo model (Abedi et al., 2021). The template analysis reported Bayesian evidence

$\omega_n=\frac{n\alpha}{32\pi M},$5

for the post-merger signal, with an excess of

$\omega_n=\frac{n\alpha}{32\pi M},$6

in gravitational-wave energy relative to the main event; the false positive probability for higher Bayes factors was

$\omega_n=\frac{n\alpha}{32\pi M},$7

while the true positive probability was

$\omega_n=\frac{n\alpha}{32\pi M},$8

and the cWB reconstruction assigned

$\omega_n=\frac{n\alpha}{32\pi M},$9

energy excess to the first echo (Abedi et al., 2021). The paper stated explicitly that the result did not reach the $k$0 standard (Abedi et al., 2021).

6. Diagnostics, degeneracies, and open problems

The most important conceptual outcome of the modern literature is that delayed repetitions are not a unique diagnostic of horizon-scale quantum structure. Echoes can arise from a near-horizon wall, from a frequency-selective quantum absorber, from a discontinuity in the metric, from a double-peaked classical potential outside a standard horizon, from caustic passage near the photon sphere, or from large-scale modified-gravity structure (Cardoso et al., 2019, Liu et al., 2021, Huang et al., 2021, Zenginoğlu et al., 2012, Momennia, 6 Feb 2025). A detection of delayed pulses therefore constrains the global scattering problem, not automatically the microscopic nature of the horizon.

Several papers propose discriminants. In the discontinuity model, when the echo period is tuned to match that of a wormhole or exotic compact object, successive maxima decay faster and the pulse front rises more suddenly than in the wormhole case; a distant environmental discontinuity also naturally gives a longer delay than a horizon-scale reflector (Liu et al., 2021). In hairy black holes, the late waveform can switch between a clear train of pulses, temporary disappearance and later reappearance of echoes, or a small number of echoes followed by a slowly decaying sinusoidal tail, depending on how the long-lived and sub-long-lived modes are excited (Guo et al., 2022). In Weyl gravity, the requirement

$k$1

already identifies a distinct large-scale origin for the second barrier (Momennia, 6 Feb 2025).

The field remains limited by idealizations. Many mechanism papers evolve scalar perturbations rather than true gravitational perturbations, work in static spherically symmetric backgrounds rather than Kerr, or replace self-consistent matter distributions by toy shells, discontinuities, or piecewise potentials (Liu et al., 2021, Guo et al., 2022, Momennia, 6 Feb 2025). On the data-analysis side, the major uncertainties remain waveform systematics, low-frequency sensitivity, look-elsewhere effects, and the treatment of non-Gaussian detector noise (Abedi et al., 2016, Abedi et al., 2020). These limitations explain why the literature contains both suggestive positive claims and strong skepticism.

In current usage, “black hole echoes” therefore names a technically diverse research area centered on repeated delayed returns in black-hole response functions. Its unifying question is not whether one specific echo mechanism exists, but which physical structures—near-horizon, environmental, geometric, optical, or stochastic—can generate delayed recurrences, how those mechanisms can be distinguished, and whether any observed signal can be mapped unambiguously back to the underlying black-hole physics.