Secondary gravitational wave signals resulting from reflections or repeated emissions from compact binary mergers.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.
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.
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.
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.
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.
| t | variable | transmission amplitude — transmission amplitude |
| r | variable | reflection amplitude — reflection amplitude |
| t_GW | variable | Gravitational wave coalescence time — coalescence time second |
| a | variable | Semi-major axis of the binary orbit — semi major axis metre |
| mu | variable | Reduced mass of the binary system — reduced mass kilogram |
| M | variable | Total mass of the binary system — total mass kilogram |
| e | variable | Eccentricity of the orbit — excentricidad |
| c | constante | Fundamental constant relating distance and time in relativity — velocidad de la luz = 299792458 metre per second |
| G | constante | Constant determining the strength of gravitational force — constante gravitacional = 6.67430e-11 cubic metre per kilogram per second squared |
| h | variable | gravitational wave strain amplitude — gravitational wave amplitude |
| M | variable | chirp mass of the binary system — chirp mass kilogram |
| f | variable | gravitational wave frequency — frecuencia hertz |
| d | variable | luminosity distance to the source — distancia metre |
| G | constante | Newtonian constant of gravitation — constante gravitacional = 6.67430e-11 cubic metre per kilogram per second squared |
| c | constante | speed of light in vacuum — velocidad de la luz = 299792458 metre per second |
| h̃_L | variable | Lensed gravitational wave signal in frequency domain — deformación de onda gravitacional |
| f | variable | Gravitational wave frequency — frecuencia hertz |
| μ_j | variable | Magnification factor of image j — magnification |
| Δt_j | variable | Time delay of image j relative to source — retardo temporal second |
| n_j | variable | Morse index of image j — morse index |
| h̃_src | variable | Unlensed source gravitational wave signal — deformación de onda gravitacional |
| ∑ | operador | Sum over lensed images — suma |
| e^{...} | operador | Complex exponential encoding phase shifts — exponential |
| h | variable | Dimensionless Hubble constant (H0/100 km/s/Mpc) — hubble constant dimensionless |
| \Omega_{\rm GW} | variable | Gravitational wave energy density parameter — energy density parameter |
| \Delta\rho/\rho | variable | Density contrast (relative density perturbation) — contraste de densidad |
| \propto | operador | Indicates proportionality between the left and right sides — proportional to |
