Catalogue of gravitational-wave echo waveforms
A repository of templates for GW echoes from exotic compact objects
(page under development)
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All material is free for use, please make reference to this webpage and to the relevant papers.
If you are interested to post other GW echo waveforms on this page please contact us. Mathematica notebooks:
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References:
Reviews:
- Adriano Testa & Paolo Pani, An analytical template for echoes, arXiv:1806.04253
- Adriano Testa, Master thesis, Sapienza University of Rome (2018)
- Vitor Cardoso & Paolo Pani, The observational evidence for horizons: from echoes to precision gravitational-wave physics - arXiv:1707.03021, Nat.Astron. 1 (2017) no.9, 586-591
- Vitor Cardoso, Seth Hopper, Caio F. B. Macedo, Carlos Palenzuela, Paolo Pani, Echoes of ECOs: gravitational-wave signatures of exotic compact objects and of quantum corrections at the horizon scale - Phys. Rev. D 94, 084031 (2016)
- Vitor Cardoso, Edgardo Franzin, Paolo Pani, Is the gravitational-wave ringdown a probe of the event horizon? - Phys. Rev. Lett. 116, 171101 (2016)
- Zachary Mark, Aaron Zimmerman, Song Ming Du, and Yanbei Chen, A recipe for echoes from exotic compact objects, Phys. Rev. D 96, 084002 (2017)
- Gaurav Khanna, http://gravity.umassd.wikispaces.net/Echoes
- Raposo, Pani, Bezares, Palenzuela, Cardoso, to appear (2018)
Reviews:
Datafiles
In the tables below, M is the total mass of the object (G=c=1 units adopted).
Only nonspinning case available at the moment.
Only nonspinning case available at the moment.
Source localized near the surface:
Prompt signal |
Reflection coefficient (R) |
Width of the cavity (d/M) |
Data/Audio |
Reference |
Ringdown (grav. polar, l=2) |
1 |
100 |
[1,2] |
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Ringdown (grav. polar, l=2) |
1 |
75 |
[1,2] |
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Ringdown (grav. polar, l=2) |
1 |
50 |
[1,2] |
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Ringdown (grav. polar, l=2) |
0.75 |
100 |
[1,2] |
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Ringdown (grav. polar, l=2) |
0.75 |
75 |
[1,2] |
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Ringdown (grav. polar, l=2) |
0.75 |
50 |
[1,2] |
|
Ringdown (grav. polar, l=2) |
0.5 |
100 |
[1,2] |
|
Ringdown (grav. polar, l=2) |
0.5 |
75 |
[1,2] |
|
Ringdown (grav. polar, l=2) |
0.5 |
50 |
[1,2] |
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Ringdown (scalar, l=2) |
1 |
100 |
[1,2] |
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Ringdown (scalar, l=2) |
1 |
75 |
[1,2] |
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Ringdown (scalar, l=2) |
1 |
50 |
[1,2] |
|
Ringdown (scalar, l=2) |
0.75 |
100 |
[1,2] |
|
Ringdown (scalar, l=2) |
0.75 |
75 |
[1,2] |
|
Ringdown (scalar, l=2) |
0.75 |
50 |
[1,2] |
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Ringdown (scalar, l=2) |
0.5 |
100 |
[1,2] |
|
Ringdown (scalar, l=2) |
0.5 |
75 |
[1,2] |
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Ringdown (scalar, l=2) |
0.5 |
50 |
[1,2] |
Point-particle source:
(gamma is the Lorentz factor of the particle at infinity)
(gamma is the Lorentz factor of the particle at infinity)
Other sources:
Wormhole: (under development)
(The reflectivity in this case is R=R_BH * Exp[-2i w x0], where R_BH is the reflection coefficient for left-moving waves scattered off a black hole, w is the frequency, x0 is the location of the throat [6])
(The reflectivity in this case is R=R_BH * Exp[-2i w x0], where R_BH is the reflection coefficient for left-moving waves scattered off a black hole, w is the frequency, x0 is the location of the throat [6])
C-stars (strongly-anisotropic stars): (under development)
(The reflectivity in this case is R=R_BH * Exp[-2i w x0], where R_BH is the reflection coefficient for left-moving waves scattered off a black hole, w is the frequency, x0 is the location of the throat [6])
(The reflectivity in this case is R=R_BH * Exp[-2i w x0], where R_BH is the reflection coefficient for left-moving waves scattered off a black hole, w is the frequency, x0 is the location of the throat [6])
Prompt signal |
Reflection coefficient (R) |
Width of the cavity (d/M) |
Audio |
Reference |
Scalar perturbation; Gaussian (r0=5M, sigma=4M) |
regularity at the center (|R|^2=1) |
corr. M/R=0.4872 |
[8] |
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Scalar perturbation; Gaussian (r0=5M, sigma=4M) |
regularity at the center (|R|^2=1) |
corr. M/R=0.4906 |
[8] |
Playing echo waveforms
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