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# Tests for the existence of black holes through gravitational wave echoes

## Abstract

The existence of black holes and spacetime singularities is a fundamental issue in science. Despite this, observations supporting their existence are scarce, and their interpretation is unclear. In this Perspective we outline the case for black holes that has been made over the past few decades, and provide an overview of how well observations adjust to this paradigm. Unsurprisingly, we conclude that observational proof for black holes is, by definition, impossible to obtain. However, just like Popper’s black swan, alternatives can be ruled out or confirmed to exist with a single observation. These observations are within reach. In the coming years and decades, we will enter an era of precision gravitational-wave physics with more sensitive detectors. Just as accelerators have required larger and larger energies to probe smaller and smaller scales, more sensitive gravitational-wave detectors will probe regions closer and closer to the horizon, potentially reaching Planck scales and beyond. What may be there, lurking?

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## References

1. Mazur, P. O. & Mottola, E. Gravitational vacuum condensate stars. Proc. Natl Acad. Sci. USA 101, 9545–9550 (2004).

2. Mathur, S. D. The fuzzball proposal for black holes: An elementary review. Fortsch. Phys. 53, 793–827 (2005).

3. Mathur, S. D. Fuzzballs and the information paradox: a summary and conjectures. Preprint at https://arxiv.org/abs/0810.4525 (2008).

4. Unruh, W. G. & Wald, R. M. Information loss. Preprint at https://arxiv.org/abs/1703.02140 (2017).

5. Broderick, A. E., Johannsen, T., Loeb, A. & Psaltis, D. Testing the no-hair theorem with event horizon telescope observations of Sagittarius A*. Astrophys. J. 784, 7 (2014).

6. Goddi, C. et al. BlackHoleCam: Fundamental physics of the Galactic center. Int. J. Mod. Phys. D 26, 1730001 (2017).

7. Ferrari, V. & Mashhoon, B. New approach to the quasinormal modes of a black hole. Phys. Rev. D 30, 295–304 (1984).

8. Cardoso, V., Miranda, A. S., Berti, E., Witek, H. & Zanchin, V. T. Geodesic stability, Lyapunov exponents and quasinormal modes. Phys. Rev. D 79, 064016 (2009).

9. Berti, E., Cardoso, V. & Starinets, A. O. Quasinormal modes of black holes and black branes. Class. Quant. Grav 26, 163001 (2009).

10. Cardoso, V., Franzin, E. & Pani, P. Is the gravitational-wave ringdown a probe of the event horizon? Phys. Rev. Lett. 116, 171101 (2016).

11. Cardoso, V., Hopper, S., Macedo, C. F. B., Palenzuela, C. & Pani, P. Gravitational-wave signatures of exotic compact objects and of quantum corrections at the horizon scale. Phys. Rev. D 94, 084031 (2016).

12. Buchdahl, H. A. General relativistic fluid spheres. Phys. Rev 116, 1027–1034 (1959).

13. Kaup, D. J. & Klein-Gordon, G. Phys. Rev 172, 1331–1342 (1968).

14. Ruffini, R. & Bonazzola, S. Systems of self-gravitating particles in general relativity and the concept of an equation of state. Phys. Rev. 187, 1767–1783 (1969).

15. Seidel, E. & Suen, W. M. Oscillating soliton stars. Phys. Rev. Lett. 66, 1659–1662 (1991).

16. Brito, R., Cardoso, V. & Okawa, H. Accretion of dark matter by stars. Phys. Rev. Lett. 115, 111301 (2015).

17. Liebling, S. L. & Palenzuela, C. Dynamical boson stars. Living Rev. Rel 15, 6 (2012).

18. Hui, L., Ostriker, J. P., Tremaine, S. & Witten, E. Ultralight scalars as cosmological dark matter. Phys. Rev. D 95, 043541 (2017).

19. Damour, T. & Solodukhin, S. N. Wormholes as black hole foils. Phys. Rev. D 76, 024016 (2007).

20. Chowdhury, B. D. & Mathur, S. D. Radiation from the non-extremal fuzzball. Class. Quant. Grav 25, 135005 (2008).

21. Mottola, E. & Vaulin, R. Macroscopic effects of the quantum trace anomaly. Phys. Rev. D 74, 064004 (2006).

22. Barcelo, C., Liberati, S., Sonego, S. & Visser, M. Black stars, not holes. Sci. Am. 301, 38–45 (2009).

23. Barcelo, C., Liberati, S., Sonego, S. & Visser, M. Fate of gravitational collapse in semiclassical gravity. Phys. Rev. D 77, 044032 (2008).

24. Gimon, E. G. & Horava, P. Astrophysical violations of the Kerr bound as a possible signature of string theory. Phys. Lett. B 672, 299–302 (2009).

25. Brustein, R. & Medved, A. J. M. Black holes as collapsed polymers. Fortsch. Phys 65, 0114 (2017).

26. Brustein, R., Medved, A. J. M. & Yagi, K. Discovering the interior of black holes. Preprint at https://arxiv.org/abs/1701.07444 (2017).

27. Holdom, B. & Ren, J. Not quite a black hole. Phys. Rev. D 95, 084034 (2017).

28. Seidel, E. & Suen, W. M. Formation of solitonic stars through gravitational cooling. Phys. Rev. Lett. 72, 2516–2519 (1994).

29. Brito, R., Cardoso, V., Macedo, C. F. B., Okawa, H. & Palenzuela, C. Interaction between bosonic dark matter and stars. Phys. Rev. D 93, 044045 (2016).

30. Keir, J. Slowly decaying waves on spherically symmetric spacetimes and ultracompact neutron stars. Class. Quant. Grav 33, 135009 (2016).

31. Cardoso, V., Crispino, L. C. B., Macedo, C. F. B., Okawa, H. & Pani, P. Light rings as observational evidence for event horizons: Long-lived modes, ergoregions and nonlinear instabilities of ultracompact objects. Phys. Rev. D 90, 044069 (2014).

32. Friedman, J. L. Generic instability of rotating relativistic stars. Commun. Math. Phys. 62, 247–278 (1978).

33. Moschidis, G. A proof of Friedman’s ergosphere instability for scalar waves. Preprint at https://arxiv.org/abs/1608.02035 (2016).

34. Cardoso, V., Pani, P., Cadoni, M. & Cavaglia, M. Ergoregion instability of ultracompact astrophysical objects. Phys. Rev. D 77, 124044 (2008).

35. Maggio, E., Pani, P. & Ferrari, V. Exotic compact objects and how to quench their ergoregion instability. Preprint at https://arxiv.org/abs/1703.03696 (2017).

36. Fritz, J. Blow-up for quasi-linear wave equations in three space dimensions. Commun. Pure Applied Math 34, 29–51 (1981).

37. Abbott, B. P. et al. Observation of gravitational waves from a binary black hole merger. Phys. Rev. Lett. 116, 061102 (2016).

38. Abbott, B. P. et al. Tests of general relativity with GW150914. Phys. Rev. Lett. 116, 221101 (2016).

39. Yunes, N. & Siemens, X. Gravitational-wave tests of general relativity with ground-based detectors and pulsar timing-arrays. Living Rev. Rel 16, 1–124 (2013).

40. Barausse, E., Cardoso, V. & Pani, P. Can environmental effects spoil precision gravitational-wave astrophysics? Phys. Rev. D 89, 104059 (2014).

41. Berti, E. et al. Testing general relativity with present and future astrophysical observations. Class. Quant. Grav 32, 243001 (2015).

42. Yunes, N., Yagi, K. & Pretorius, F. Theoretical physics implications of the binary black-hole mergers GW150914 and GW151226. Phys. Rev. D 94, 084002 (2016).

43. Maselli, A. et al. Probing Planckian corrections at the horizon scale with LISA binaries. Preprint at https://arxiv.org/abs/1703.10612 (2017).

44. Abbott, B. P. et al. GW151226: Observation of gravitational waves from a 22-solar-mass binary black hole coalescence. Phys. Rev. Lett. 116, 241103 (2016).

45. Buonanno, A., Cook, G. B. & Pretorius, F. Inspiral, merger and ring-down of equal-mass black-hole binaries. Phys. Rev. D 75, 124018 (2007).

46. Berti, E. et al. Inspiral, merger and ringdown of unequal mass black hole binaries: A multipolar analysis. Phys. Rev. D 76, 064034 (2007).

47. Sperhake, U., Berti, E. & Cardoso, V. Numerical simulations of black-hole binaries and gravitational wave emission. C. R. Phys. 14, 306–317 (2013).

48. Blanchet, L. Gravitational radiation from post-newtonian sources and inspiralling compact binaries. Living Rev. Rel 17, 2 (2014).

49. Price, R. H. & Khanna, G. Gravitational wave sources: reflections and echoes. Preprint at https://arxiv.org/abs/1702.04833 (2017).

50. Nakano, H., Sago, N., Tagoshi, H. & Tanaka, T. Black hole ringdown echoes and howls. Prog. Theor. Exp. Phys. 2017, 071E01 (2017).

51. Abbott, B. P. et al. Search for gravitational wave ringdowns from perturbed black holes in LIGO S4 data. Phys. Rev. D 80, 062001 (2009).

52. Berti, E., Sesana, A., Barausse, E., Cardoso, V. & Belczynski, K. Spectroscopy of Kerr black holes with Earth- and space-based interferometers. Phys. Rev. Lett. 117, 101102 (2016).

53. Amaro-Seoane, P. et al. Laser interferometer space antenna. Preprint at https://arxiv.org/abs/1702.00786 (2017).

54. Punturo, M. et al. The Einstein telescope: A third-generation gravitational wave observatory. Class. Quant. Grav 27, 194002 (2010).

55. LIGO Scientific Collaboration. LIGO Instrument Science White Paper (LIGO, 2015); https://dcc.ligo.org/public/0120/T1500290/002/T1500290.pdf

56. Abedi, J., Dykaar, H. & Afshordi, N. Echoes from the abyss: Evidence for Planck-scale structure at black hole horizons. Preprint at https://arxiv.org/abs/1612.00266 (2016).

57. Ashton, G. et al. Comments on: ‘Echoes from the abyss: Evidence for Planck-scale structure at black hole horizons’. Preprint at https://arxiv.org/abs/1612.05625 (2016).

58. Abedi, J., Dykaar, H. & Afshordi, N. Echoes from the abyss: The holiday edition! Preprint at https://arxiv.org/abs/1701.03485 (2017).

59. Mark, Z., Zimmerman, A., Du, S. M. & Chen, Y. A recipe for echoes from exotic compact objects. Preprint at https://arxiv.org/abs/1706.06155 (2017).

60. Mottola, E. Scalar gravitational waves in the effective theory of gravity. J. High Energy Phys. 2017, 43 (2017).

61. Pani, P., Berti, E., Cardoso, V., Chen, Y. & Norte, R. Gravitational-wave signatures of the absence of an event horizon. II. Extreme mass ratio inspirals in the spacetime of a thin-shell gravastar. Phys. Rev. D 81, 084011 (2010).

62. Macedo, C. F. B., Pani, P., Cardoso, V. & Crispino, L. C. B. Into the lair: Gravitational-wave signatures of dark matter. Astrophys. J. 774, 48 (2013).

63. Macedo, C. F. B., Pani, P., Cardoso, V. & Crispino, L. C. B. Astrophysical signatures of boson stars: Quasinormal modes and inspiral resonances. Phys. Rev. D 88, 064046 (2013).

64. Berti, E., Cardoso, V. & Will, C. M. On gravitational-wave spectroscopy of massive black holes with the space interferometer LISA. Phys. Rev. D 73, 064030 (2006).

65. Berti, E. & Cardoso, V. Supermassive black holes or boson stars? Hair counting with gravitational wave detectors. Int. J. Mod. Phys. D 15, 2209–2216 (2006).

66. Chirenti, C. & Rezzolla, L. Did GW150914 produce a rotating gravastar? Phys. Rev. D 94, 084016 (2016).

67. Konoplya, R. A. & Zhidenko, A. Wormholes versus black holes: Quasinormal ringing at early and late times. J. Cosmol. Astropart. Phys. 1612, 043 (2016).

68. Nandi, K. K., Izmailov, R. N., Yanbekov, A. A. & Shayakhmetov, A. A. Ring-down gravitational waves and lensing observables: How far can a wormhole mimic those of a black hole? Phys. Rev. D 95, 104011 (2017).

69. Barcelo, C., Carballo-Rubio, R. & Garay, L. J. Gravitational wave echoes from macroscopic quantum gravity effects. J. High Energ. Phys. 2017, 54 (2017).

70. Brustein, R., Medved, A. J. M. & Yagi, K. When black holes collide: Probing the interior composition by the spectrum of ringdown modes and emitted gravitational waves. Preprint at https://arxiv.org/abs/1704.05789 (2017).

71. Bezares, M., Palenzuela, C. & Bona, C. Final fate of compact boson star mergers. Phys. Rev. D 95, 124005 (2017).

72. Cardoso, V., Franzin, E., Maselli, A., Pani, P. & Raposo, G. Testing strong-field gravity with tidal Love numbers. Phys. Rev. D 95, 084014 (2017).

73. Flanagan, E. E. & Hinderer, T. Constraining neutron star tidal Love numbers with gravitational wave detectors. Phys. Rev. D 77, 021502 (2008).

74. Binnington, T. & Poisson, E. Relativistic theory of tidal Love numbers. Phys. Rev. D 80, 084018 (2009).

75. Damour, T. & Nagar, A. Relativistic tidal properties of neutron stars. Phys. Rev. D 80, 084035 (2009).

76. Poisson, E. Tidal deformation of a slowly rotating black hole. Phys. Rev. D 91, 044004 (2015).

77. Pani, P., Gualtieri, L., Maselli, A. & Ferrari, V. Tidal deformations of a spinning compact object. Phys. Rev. D 92, 024010 (2015).

78. Wade, M., Creighton, J. D. E., Ochsner, E. & Nielsen, A. B. Advanced LIGO’s ability to detect apparent violations of the cosmic censorship conjecture and the no-hair theorem through compact binary coalescence detections. Phys. Rev. D 88, 083002 (2013).

79. Sennett, N., Hinderer, T., Steinhoff, J., Buonanno, A. & Ossokine, S. Distinguishing boson stars from black holes and neutron stars from tidal interactions in inspiraling binary systems. Phys. Rev. D 96, 024002 (2017).

80. Krishnendu, N. V., Arun, K. G. & Mishra, C. K. Testing the binary black hole nature of a compact binary coalescence. Preprint at https://arxiv.org/abs/1701.06318 (2017).

81. Birks, J. B. Rutherford at Manchester. (Benjamon, New York, 1963).

## Acknowledgements

V.C. acknowledges financial support provided under the European Union’s H2020 ERC Consolidator Grant ‘Matter and strong-field gravity: New frontiers in Einstein’s theory’, grant agreement No. MaGRaTh–646597. Research at Perimeter Institute is supported by the Government of Canada through Industry Canada and the Province of Ontario through the Ministry of Economic Development Innovation. This article is based on work from COST Action CA16104 ‘GWverse’ and MP1304 ‘NewCompstar’, supported by COST (European Cooperation in Science and Technology). This work was partially supported by FCT-Portugal through project IF/00293/2013, and by the H2020-MSCA-RISE-2015, grant No. StronGrHEP-690904.

## Author information

Authors

### Contributions

V.C. and P.P. contributed equally to the writing and calculations in this work.

### Corresponding author

Correspondence to Vitor Cardoso.

## Ethics declarations

### Competing interests

The authors declare no competing financial interests.

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Cardoso, V., Pani, P. Tests for the existence of black holes through gravitational wave echoes. Nat Astron 1, 586–591 (2017). https://doi.org/10.1038/s41550-017-0225-y

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• DOI: https://doi.org/10.1038/s41550-017-0225-y

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