phenomenon

gravitational wave echo

Secondary gravitational wave signals resulting from reflections or repeated emissions from compact binary mergers.
9 related articles · 5 formulas

Description

Gravitational wave echoes are hypothetical secondary signals that could follow the main gravitational wave burst from a compact binary merger, such as the collision of two black holes or neutron stars. While the primary signal is a strong, characteristic chirp produced by the inspiral and merger, echoes would appear as a series of weaker, repeating pulses shortly after. They are not part of standard general relativity predictions for black holes, which suggest that anything crossing the event horizon is lost and no further radiation escapes.

History

The concept gained prominence after the first LIGO detection in 2015, when a team led by Niayesh Afshordi and Vitor Cardoso proposed in 2016 that echoes could be a signature of quantum structure near black hole horizons. No confirmed detection has been made as of 2025.

How it works

The standard picture of a black hole merger ends with a single, distorted black hole that rings down, emitting gravitational waves at characteristic quasinormal frequencies that decay exponentially. Echoes would arise if the merged object is not a classical black hole but has some structure near the would-be horizon — for example, an exotic compact object with a reflective surface or a firewall. In that case, part of the gravitational wave energy would be reflected back and forth between the inner structure and the potential barrier outside, leaking out as a series of delayed pulses. The time delay between echoes would encode the size of the reflecting region, potentially revealing quantum gravity effects at the horizon scale.

In practice

Searching for echoes in LIGO and Virgo data is an active area of research that tests the classical black hole paradigm and probes quantum gravity, though no definitive detection has been reported.

Fun fact

If echoes exist, they would imply that black holes are not truly black but have a 'quantum hair' that reflects gravitational waves, potentially resolving the information paradox.

Concept graph →

Formulas

$$|t|^2 + |r|^2 = 1$$
The sum of transmitted and reflected intensities equals the incident intensity.
What is in the formula
tvariabletransmission amplitude — transmission amplitude
rvariablereflection amplitude — reflection amplitude
|t|^2+|r|^2=1 · 2605.11065v1
$$t_{\mathrm{GW}} = \frac{5}{256} \frac{c^5 a^4}{G^3 \mu M^2} (1-e^2)^{7/2}$$
Time for binary to coalesce due to gravitational wave emission.
What is in the formula
t_GWvariableGravitational wave coalescence time — coalescence time second
avariableSemi-major axis of the binary orbit — semi major axis metre
muvariableReduced mass of the binary system — reduced mass kilogram
MvariableTotal mass of the binary system — total mass kilogram
evariableEccentricity of the orbit — eccentricity
cconstantFundamental constant relating distance and time in relativity — speed of light = 299792458 metre per second
GconstantConstant determining the strength of gravitational force — gravitational constant = 6.67430e-11 cubic metre per kilogram per second squared
t_{{gw}}=\frac{5}{256}\frac{c^5a^4}{g^3μm^2}(1-e^2)^{7/2} · 2607.04121v1
$$h = \frac{4 G^{5/3} \mathcal{M}^{5/3} (\pi f)^{2/3}}{c^4 d}$$
Amplitude depends on chirp mass, frequency, and distance.
What is in the formula
hvariablegravitational wave strain amplitude — gravitational wave amplitude
Mvariablechirp mass of the binary system — chirp mass kilogram
fvariablegravitational wave frequency — frequency hertz
dvariableluminosity distance to the source — distance metre
GconstantNewtonian constant of gravitation — gravitational constant = 6.67430e-11 cubic metre per kilogram per second squared
cconstantspeed of light in vacuum — speed of light = 299792458 metre per second
a=\frac{2(gm_c)^{5/3}}{c^4d_l}(πf_0)^{2/3} · 2606.29039
$$\tilde{h}_L(f) = \sum_j |\mu_j|^{1/2} e^{2\pi i f \Delta t_j - i\pi n_j} \tilde{h}_{\rm src}(f)$$
Lensed gravitational wave signal sum over images.
What is in the formula
h̃_LvariableLensed gravitational wave signal in frequency domain — gravitational wave strain
fvariableGravitational wave frequency — frequency hertz
μ_jvariableMagnification factor of image j — magnification
Δt_jvariableTime delay of image j relative to source — time delay second
n_jvariableMorse index of image j — morse index
h̃_srcvariableUnlensed source gravitational wave signal — gravitational wave strain
∑operatorSum over lensed images — summation
e^{...}operatorComplex exponential encoding phase shifts — exponential
\tilde{h}_l(f)=\sum_{j=1}^{n_{\rmimg}}|μ_j|^{1/2}\exp[2πifδt_j-iπn_j]\tilde{h}_{\rmsrc}(f;θ_s) · 2607.03885
$$h^2 \Omega_{\rm GW} \propto \left(\frac{\Delta\rho}{\rho}\right)^2$$
Gravitational wave amplitude scales with density contrast squared.
What is in the formula
hvariableDimensionless Hubble constant (H0/100 km/s/Mpc) — hubble constant dimensionless
\Omega_{\rm GW}variableGravitational wave energy density parameter — energy density parameter
\Delta\rho/\rhovariableDensity contrast (relative density perturbation) — density contrast
\proptooperatorIndicates proportionality between the left and right sides — proportional to
h^2ω_{\rmgw}^{\rmpeak}\sim10^{-8}\frac{δρ^2}{ρ_f^2} · 2607.24734v1

Related articles · 9

General Relativity2026-07-192 minarXiv:2607.17431express
Gravitational Waves with a Space-Time Correction
When two black holes merge far away, we receive a tremor of space — gravitational waves. Usually, they are described by Einstein's equations, but what if gravity works differently at the tiniest distances? The authors took one such hypothesis — Hořava–Lifshitz gravity.
15 Solar Masses: The Spin Frontier of Black Holes
The mergers of black holes, first predicted by Karl Schwarzschild, are the main source of gravitational waves picked up by LIGO detectors. Over the years, 259 events have accumulated, each one an encrypted birth story of a pair. But is there a hidden system in this data?
High Energy2026-06-102 minarXiv:2606.12205express
The Hidden Spin of Black Holes
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General Relativity2026-05-261 minarXiv:2605.27225express
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Twin Black Holes: Why Light Ones Are Lazy and Heavy Ones Are Tops
Two figure skaters glide on the ice. One is light and cautious, barely rotating. The other is massive and fast, spinning with all its might, and in different directions at that. That's roughly the picture painted by gravitational waves from black hole mergers.
High Energy2026-05-121 minarXiv:2605.11947express
How the elongated merger orbit points to where the pair was born
When a neutron star and a black hole merge, they send out gravitational waves — ripples in spacetime that reach Earth. These ripples carry the imprint of their final dance: the orbit before the collision is often elongated, like an ellipse.
General Relativity2026-04-162 minarXiv:2604.15431express
The Dance of Black Holes on Stretched Orbits
Two black holes spiral around each other not in a smooth dance, but like two stones thrown from opposite banks into a deep whirlpool. Their orbit resembles a highly flattened oval — the eccentricity is nearly one. When they finally collide, a powerful burst of gravitational waves is born — a shudder of space itself.
General Relativity2026-04-102 minarXiv:2604.09828express
How Gravitational Waves Test Black Holes for 'Purity'
When two black holes spiral around each other and merge, they send ripples across the universe — gravitational waves. These waves carry the imprint of exactly how the objects moved before the collision. From the shape of this 'dance,' you can tell how closely the objects resemble perfect black holes.
Instrumentation2026-01-302 minarXiv:2602.00203express
Waves Squeeze Time
Two black holes whirl faster and faster, draw closer, and merge into one. The space around them trembles — that tremor travels across the universe for billions of years and finally makes detector mirrors sway by a fraction of an atom. Scientists catch this signal and want to know exactly which holes produced it.