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Fuzzballs and observations

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Abstract

The advent of gravitational waves and black hole imaging has opened a new window into probing the horizon scale of black holes. An important question is whether string theory results for black holes can predict interesting and observable features that current and future experiments can probe. In this article I review the budding and exciting research being done on understanding the possibilities of observing signals from fuzzballs, where black holes are replaced by string-theoretic horizon-scale microstructure. In order to be accessible to both string theorists and black hole phenomenologists, I give a brief overview of the relevant observational experiments as well as the fuzzball paradigm in string theory and its explicitly constructable solutions called microstate geometries.

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Notes

  1. An alternative to \(\epsilon \) is to define a length scale \(R_a\) at which there are large modifications to the standard evolution. This is to be considered in conjunction with a second, “hardness” length scale L, which indicates the scale on which these new, modification effects vary [7,8,9]. Such “hardness” has been conjectured to be important in determining the energy that quanta must have in order to see effects from the non-trivial fuzzball structure [10].

  2. Note that Buchdahl’s theorem in pure general relativity would imply \(\epsilon \ge 1/8\) for static, spherically symmetric ECOs, when we take \(r_h=2M\) to be the Schwarzschild radius [5, 11].

  3. Note that this refers to Solodukhin-type wormholes [12] obtained by changing black hole metrics by hand, rather than the recent ones constructed in string theory such as in [13, 14].

  4. Mergers of neutron stars also produce gravitational waves; this was first observed in 2017 [23]. I will focus here on black hole (or ECO) mergers.

  5. I am being a bit loose with the terminology here. The actual shadow of the black hole is usually defined to be the dark circular region in the center of the image of the black hole, which is actually not much influenced by the accretion disc [29]. The outer edge of the shadow is called the photon ring; for Schwarschild, this is \(r_\mathrm{ph} =\sqrt{27} M\). The properties of this photon ring, if measured, can give very precise information on the black hole and any possible horizon-scale structure [29,30,31,32,33].

  6. The main uncertainty in model selection is not due to the underlying spacetime, of which it is pretty clear it must be (close to) the Kerr black hole spacetime. Rather, the details of the event horizon are effectively blurred by the complex physics of the accretion disc plasma [39]. For example, the electrons can emit non-thermal radiation that is not accounted for in most simulations, leading to flares and hot spots [40,41,42,43,44]. This also makes it hard to detect or extract features of any possible horizon-scale microstructure replacing the black hole in the spacetime [45]. Note that accretion disc plasma physics effects may also blur the ability of gravitational wave observations to perform precision strong-field gravity tests [46]. (Many thanks to B. Ripperda for elaborating this issue to me.)

  7. One would perhaps expect quantum corrections at inner horizons, which are Cauchy horizons and may be subject to quantum instabilities [75, 76].

  8. Not all centers are smooth in five dimensions; the charges or parameters of a center must obey certain conditions in order to avoid being singular [83].

  9. The quantized number of D1, D5, P excitations is related to the supergravity charges as \(Q_1 = ((2\pi )^4 g_s \alpha '^3/V_4)\, N_1\), \(Q_5 = (g_s \alpha ')\, N_5\), and \(Q_P = (\alpha '^4/(V_4 R_y^2))\, N_P\), where \(g_s\) is the (ten-dimensional) string coupling, \(\alpha '=l_s^2\) is the string length squared, and \(V_4\) is the volume of the compact four-dimensional manifold (\(T^4\) or K3) that the D5-branes wrap.

  10. Even here, the Lunin–Mathur geometries with the most typical supertube profile are of a stringy size and so fall outside of the regime where the supergravity approximation is valid. Moreover, the most typical states will be quantum superpositions of the states described by these Lunin–Mathur supertube geometries and so are not themselves described by a geometry [17, 81, 82, 134]. Additionally, the D1/D5 system does not correspond to a black hole of finite size; rather, the ensemble of D1/D5 states corresponds to a singular geometry where the would-be horizon has zero size.

  11. Unfortunately, there is some overloading of the terms “light ring” or “photon ring” in the literature. The conventions followed by the EHT collaboration [2, 29, 34] are that the photon ring is the edge of the black hole shadow—for Schwarschild, this is \(r=\sqrt{27}M\); see also footnote 6. However, in most gravitational wave papers such as [143], the convention is that the light ring is the smallest photon orbit radius, which for Schwarzschild is \(r=3M\).

  12. This size is measured in an appropriate tortoise coordinate (which corresponds to the travel time of a null geodesic), see section 4.1 in [143].

  13. In [5], \(\ell \) is a four-dimensional wavenumber. The same scaling also holds in five dimensions as well [6].

  14. A more complete list of references regarding the discussions on the claims of echo observations can be found in e.g. [6], at the start of section 1.

  15. Note that [166, 167] considers multicentered microstate geometries where the centers are not necessarily on a line and thus a more general version of the axisymmetric multipole formulae (6)–(7) must be used. Here, I will simply adjust the nomenclature of [166, 167] to the axisymmetric notation using only \(M_\ell ,S_\ell \) (instead of general \(M_{\ell m},S_{\ell m}\)) for simplicity of presentation.

  16. The correct definition of the magnetic Love numbers was only recently clarified [172].

  17. Various statements can be found in the literature such as “The tidal Love numbers of black holes in four dimensions vanish”; I wish to emphasize that, to the best of my knowledge, this has only been convincingly proven for static black holes in Einstein-Maxwell gravity. It has also been shown that the Love numbers vanish for axisymmetric perturbations of slowly rotating black holes [176, 177]. Recently, it has been argued that more general gravitational perturbations lead to non-zero Love numbers for Kerr [178], although [179] claims that the Kerr Love numbers do vanish when the correct boundary conditions are used. Note also that generically, black holes in alternative theories of gravity do not have vanishing Love numbers [169, 180, 181]. See also section 1 of [182] and references therein for an overview.

  18. Null geodesics in single-mode (1, 0, n) and (2, 1, n) superstrata geometries have remarkable integrability properties [189, 190], making it feasible to study their properties (semi-)analytically.

  19. Relatedly, there is a Penrose process for microstate geometries [195, 196].

  20. Certain non-supersymmetric microstate geometries, having an actual ergoregion, can be shown to be linearly unstable [197].

  21. I wish to thank R. Walker for discussions on this point.

  22. Thermalization in the D1/D5 system from the dual CFT point of view and in the context of fuzzballs was discussed in [204].

References

  1. Abbott, B.P., et al.: LIGO: the laser interferometer gravitational-wave observatory. Rep. Progress Phys. 72, 076901 (2009)

    Article  ADS  Google Scholar 

  2. Event Horizon Telescope Collaboration, Akiyama, K., et al., First M87 event horizon telescope results. I. The shadow of the supermassive black hole. Astrophys. J. 875(1), L1 (2019). arXiv:1906.11238

  3. Cardoso, V., Pani, P.: The observational evidence for horizons: from echoes to precision gravitational-wave physics. arXiv:1707.03021

  4. Cardoso, V., Pani, P.: Tests for the existence of black holes through gravitational wave echoes. Nat. Astron. 1(9), 586–591 (2017). arXiv:1709.01525

  5. Cardoso, V., Pani, P.: Testing the nature of dark compact objects: a status report. Liv. Rev. Rel. 22(1), 4 (2019). arXiv:1904.05363

  6. Dimitrov, V., Lemmens, T., Mayerson, D.R., Min, V.S., Vercnocke, B.: Gravitational waves, holography, and black hole microstates. arXiv:2007.01879

  7. Giddings, S.B.: Possible observational windows for quantum effects from black holes. Phys. Rev. D 90(12), 124033 (2014). arXiv:1406.7001

  8. Giddings, S.B.: Gravitational wave tests of quantum modifications to black hole structure—with post-GW150914 update. Class. Quant. Grav. 33(23), 235010 (2016). arXiv:1602.03622

  9. Giddings, S.B., Koren, S., Treviño, G.: Exploring strong-field deviations from general relativity via gravitational waves. Phys. Rev. D 100(4), 044005 (2019). arXiv:1904.04258

  10. Mathur, S.D.: The VECRO hypothesis. arXiv:2001.11057

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

    Article  ADS  MathSciNet  MATH  Google Scholar 

  12. Solodukhin, S.N.: Restoring unitarity in BTZ black hole. Phys. Rev. D 71, 064006 (2005). arXiv:hep-th/0501053

    Article  ADS  MathSciNet  Google Scholar 

  13. Gao, P., Jafferis, D.L., Wall, A.C.: Traversable wormholes via a double trace deformation. JHEP 12, 151 (2017). arXiv:1608.05687

    Article  ADS  MathSciNet  MATH  Google Scholar 

  14. Maldacena, J., Milekhin, A.: Humanly traversable wormholes. arXiv:2008.06618

  15. Kaup, D.J.: Klein–Gordon Geon. Phys. Rev. 172, 1331–1342 (1968)

    Article  ADS  Google Scholar 

  16. 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)

    Article  ADS  Google Scholar 

  17. Mathur, S.D.: The Fuzzball proposal for black holes: an elementary review. Fortsch. Phys. 53, 793–827 (2005). arXiv:hep-th/0502050

    Article  ADS  MathSciNet  MATH  Google Scholar 

  18. Bena, I., Wang, C.-W., Warner, N.P.: Mergers and typical black hole microstates. JHEP 11, 042 (2006). arXiv:hep-th/0608217

    Article  ADS  MathSciNet  Google Scholar 

  19. Bena, I., Giusto, S., Martinec, E.J., Russo, R., Shigemori, M., Turton, D., Warner, N.P.: Asymptotically-flat supergravity solutions deep inside the black-hole regime. JHEP 02, 014 (2018). arXiv:1711.10474

    Article  ADS  MathSciNet  MATH  Google Scholar 

  20. Gibbons, G., Warner, N.: Global structure of five-dimensional fuzzballs. Class. Quant. Grav. 31, 025016 (2014). arXiv:1305.0957

    Article  ADS  MATH  Google Scholar 

  21. de Lange, P., Mayerson, D.R., Vercnocke, B.: Structure of six-dimensional microstate geometries. JHEP 09, 075 (2015). arXiv:1504.07987

    Article  MathSciNet  MATH  Google Scholar 

  22. LIGO Scientific, Virgo Collaboration, Abbott, B., et al.: Observation of gravitational waves from a binary black hole merger. Phys. Rev. Lett. 116(6), 061102 (2016). arXiv:1602.03837

  23. LIGO Scientific, Virgo Collaboration, Abbott, B., et al.: GW170817: observation of gravitational waves from a binary neutron star inspiral. Phys. Rev. Lett. 119(16), 161101 (2017). arXiv:1710.05832

  24. Danzmann, K., The LISA Study Team: LISA: laser interferometer space antenna for gravitational wave measurements. Class. Quantum Grav. 13, A247–A250 (1996)

  25. LISA Collaboration, Amaro-Seoane, P., et al.: Laser interferometer space antenna. arXiv:1702.00786

  26. Babak, S., Gair, J., Sesana, A., Barausse, E., Sopuerta, C.F., Berry, C.P., Berti, E., Amaro-Seoane, P., Petiteau, A., Klein, A.: Science with the space-based interferometer LISA. V: Extreme mass-ratio inspirals. Phys. Rev. D 95(10), 103012 (2017). arXiv:1703.09722

  27. Miller, M.C.: Gravitational waves: dawn of a new astronomy. Nature 531, 40–42 (2016)

    Article  ADS  Google Scholar 

  28. Barack, L., et al.: Black holes, gravitational waves and fundamental physics: a roadmap. Class. Quant. Grav. 36(14), 143001 (2019). arXiv:1806.05195

  29. Narayan, R., Johnson, M.D., Gammie, C.F.: The shadow of a spherically accreting black hole. Astrophys. J. Lett. 885(2), L33 (2019). arXiv:1910.02957

  30. Gralla, S.E., Lupsasca, A., Marrone, D.P.: The shape of the black hole photon ring: a precise test of strong-field general relativity. arXiv:2008.03879

  31. Gralla, S.E., Lupsasca, A.: On the observable shape of black hole photon rings. arXiv:2007.10336

  32. Gralla, S.E.: Measuring the shape of a black hole photon ring. Phys. Rev. D 102(4), 044017 (2020). arXiv:2005.03856

  33. Johnson, M.D., et al.: Universal interferometric signatures of a black hole’s photon ring. arXiv:1907.04329

  34. Event Horizon Telescope Collaboration, Akiyama, K., et al.: First M87 event horizon telescope results. V. Physical origin of the asymmetric ring. Astrophys. J. Lett. 875(1), L5 (2019). arXiv:1906.11242

  35. Gralla, S.E., Holz, D.E., Wald, R.M.: Black hole shadows, photon rings, and lensing rings. Phys. Rev. D 100 (2019)

  36. Porth, O., Event Horizon Telescope Collaboration, et al.: The event horizon general relativistic magnetohydrodynamic code comparison project. ApJS 243, 26 (2019). arXiv:1904.04923

  37. Gold, R., Event Horizon Telescope Collaboration, et al.: Verification of radiative transfer schemes for the EHT. ApJ 897, 148 (2020)

  38. Event Horizon Telescope Collaboration, Psaltis, D., et al.: Gravitational test beyond the first post-Newtonian order with the shadow of the M87 black hole. Phys. Rev. Lett. 125(14), 141104 (2020). arXiv:2010.01055

  39. Gralla, S.E., Holz, D.E., Wald, R.M.: Black hole shadows, photon rings, and lensing rings. Phys. Rev. D 100(2), 024018 (2019). arXiv:1906.00873

  40. Sironi, L., Spitkovsky, A.: Relativistic reconnection: an efficient source of non-thermal particles. Astrophys. J. Lett. 783, L21 (2014). arXiv:1401.5471

    Article  ADS  Google Scholar 

  41. Ponti, G., et al.: A powerful flare from Sgr A* confirms the synchrotron nature of the X-ray emission. Mon. Not. Roy. Astron. Soc. 468(2), 2447–2468 (2017). arXiv:1703.03410

  42. Dodds-Eden, K., Sharma, P., Quataert, E., Genzel, R., Gillessen, S., Eisenhauer, F., Porquet, D.: Time dependent models of flares from sagittarius A*. Astrophys. J. 725, 450–465 (2010). arXiv:1005.0389

    Article  ADS  Google Scholar 

  43. GRAVITY Collaboration, Abuter, R., et al.: Detection of orbital motions near the last stable circular orbit of the massive black hole SgrA*. A&A 618, L10 (2018)

  44. Ripperda, B., Bacchini, F., Philippov, A.: Magnetic reconnection and hot spot formation in black hole accretion disks. Astrophys. J. 900(2), 100 (2020). arXiv:2003.04330

  45. Gralla, S.E.: Can the EHT M87 results be used to test general relativity?. arXiv:2010.08557

  46. Cardoso, V., Guo, W.-d., Macedo, C.F., Pani, P.: The tune of the universe: the role of plasma in tests of strong-field gravity. arXiv:2009.07287

  47. Giddings, S.B., Psaltis, D.: Event horizon telescope observations as probes for quantum structure of astrophysical black holes. Phys. Rev. D 97(8), 084035 (2018). arXiv:1606.07814

  48. Giddings, S.B.: Searching for quantum black hole structure with the event horizon telescope. Universe 5(9), 201 (2019). arXiv:1904.05287

  49. Vazquez, S.E., Esteban, E.P.: Strong field gravitational lensing by a Kerr black hole. Nuovo Cim. B 119, 489–519 (2004). arXiv:gr-qc/0308023

    ADS  MathSciNet  Google Scholar 

  50. Amarilla, L., Eiroa, E.F.: Shadows of rotating black holes in alternative theories. In 14th Marcel Grossmann Meeting on Recent Developments in Theoretical and Experimental General Relativity, Astrophysics, and Relativistic Field Theories, vol. 4, pp. 3543–3548 (2017). arXiv:1512.08956

  51. Virbhadra, K., Ellis, G.F.: Schwarzschild black hole lensing. Phys. Rev. D 62, 084003 (2000). arXiv:astro-ph/9904193

    Article  ADS  MathSciNet  Google Scholar 

  52. Israel, W.: Event horizons in static vacuum space–times. Phys. Rev. 164, 1776–1779 (1967)

    Article  ADS  Google Scholar 

  53. Carter, B.: Axisymmetric black hole has only two degrees of freedom. Phys. Rev. Lett. 26, 331–333 (1971)

    Article  ADS  Google Scholar 

  54. Bekenstein, J.D.: Nonexistence of Baryon number for static black holes. Phys. Rev. D 5, 1239–1246 (1972)

    Article  ADS  MathSciNet  Google Scholar 

  55. Mazur, P.O.: Black hole uniqueness theorems. arXiv:hep-th/0101012

  56. Hawking, S.: Particle creation by black holes. Commun. Math. Phys. 43, 199–220 (1975). [Erratum: Commun.Math.Phys. 46, 206 (1976)]

  57. Mathur, S.D.: Resolving the black hole causality paradox. Gen. Rel. Grav. 51(2), 24 (2019). arXiv:1703.03042

  58. Mathur, S.D.: The information paradox: a pedagogical introduction. Class. Quant. Grav. 26, 224001 (2009). arXiv:0909.1038

    Article  ADS  MathSciNet  MATH  Google Scholar 

  59. Almheiri, A., Marolf, D., Polchinski, J., Sully, J.: Black holes: complementarity or firewalls? JHEP 02, 062 (2013). arXiv:1207.3123

    Article  ADS  MathSciNet  MATH  Google Scholar 

  60. Mathur, S.D., Turton, D.: The flaw in the firewall argument. Nucl. Phys. B 884, 566–611 (2014). arXiv:1306.5488

    Article  ADS  MATH  Google Scholar 

  61. Papadodimas, K., Raju, S.: An infalling observer in AdS/CFT. JHEP 10, 212 (2013). arXiv:1211.6767

    Article  ADS  Google Scholar 

  62. Papadodimas, K., Raju, S.: tState-dependent bulk-boundary maps and black hole complementarity. Phys. Rev. D 89(8), 086010 (2014). arXiv:1310.6335

  63. Papadodimas, K., Raju, S.: Black hole interior in the holographic correspondence and the information paradox. Phys. Rev. Lett. 112(5), 051301 (2014). arXiv:1310.6334

  64. Papadodimas, K., Raju, S.: Remarks on the necessity and implications of state-dependence in the black hole interior. Phys. Rev. D 93(8), 084049 (2016). arXiv:1503.08825

  65. Almheiri, A., Engelhardt, N., Marolf, D., Maxfield, H.: The entropy of bulk quantum fields and the entanglement wedge of an evaporating black hole. JHEP 12, 063 (2019). arXiv:1905.08762

    Article  ADS  MathSciNet  MATH  Google Scholar 

  66. Almheiri, A., Mahajan, R., Maldacena, J., Zhao, Y.: The page curve of Hawking radiation from semiclassical geometry. JHEP 03, 149 (2020). arXiv:1908.10996

    Article  ADS  MathSciNet  MATH  Google Scholar 

  67. Penington, G.: Entanglement wedge reconstruction and the information paradox. JHEP 09, 002 (2020). arXiv:1905.08255

    Article  ADS  Google Scholar 

  68. Almheiri, A., Mahajan, R., Maldacena, J.: Islands outside the horizon. arXiv:1910.11077

  69. Giddings, S.B.: Black hole information, unitarity, and nonlocality. Phys. Rev. D 74, 106005 (2006). arXiv:hep-th/0605196

    Article  ADS  MathSciNet  Google Scholar 

  70. Giddings, S.B.: Black holes, quantum information, and unitary evolution. Phys. Rev. D 85, 124063 (2012). arXiv:1201.1037

    Article  ADS  Google Scholar 

  71. Giddings, S.B.: Nonviolent nonlocality. Phys. Rev. D 88, 064023 (2013). arXiv:1211.7070

    Article  ADS  Google Scholar 

  72. Giddings, S.B.: Nonviolent information transfer from black holes: a field theory parametrization. Phys. Rev. D 88(2), 024018 (2013). arXiv:1302.2613

  73. Giddings, S.B.: Observational strong gravity and quantum black hole structure. Int. J. Mod. Phys. D 25(12), 1644014 (2016). arXiv:1605.05341

  74. Guo, B., Hampton, S., Mathur, S.D.: Can we observe fuzzballs or firewalls? JHEP 07, 162 (2018). arXiv:1711.01617

    Article  ADS  MathSciNet  MATH  Google Scholar 

  75. Hollands, S., Wald, R.M., Zahn, J.: Quantum instability of the Cauchy horizon in Reissner–Nordström–deSitter space–time. Class. Quantum Grav. 37(11), 115009 (2020). arXiv:1912.06047

  76. Penrose, R.: Gravitational collapse (invited Paper). In: Dewitt-Morette, C. (ed.) Gravitational Radiation and Gravitational Collapse, vol. 64, p. 82 (1974)

  77. Kraus, P., Mathur, S.D.: Nature abhors a horizon. Int. J. Mod. Phys. D 24(12), 1543003 (2015). arXiv:1505.05078

  78. Mathur, S.D.: Tunneling into fuzzball states. Gen. Rel. Grav. 42, 113–118 (2010). arXiv:0805.3716

    Article  ADS  MathSciNet  MATH  Google Scholar 

  79. Mathur, S.D.: How fast can a black hole release its information? Int. J. Mod. Phys. D 18, 2215–2219 (2009). arXiv:0905.4483

    Article  ADS  MathSciNet  MATH  Google Scholar 

  80. Bena, I., Warner, N.P.: Resolving the structure of black holes: philosophizing with a hammer. arXiv:1311.4538

  81. Chen, F., Michel, B., Polchinski, J., Puhm, A.: Journey to the Center of the Fuzzball. JHEP 02, 081 (2015). arXiv:1408.4798

    Article  ADS  MathSciNet  MATH  Google Scholar 

  82. Raju, S., Shrivastava, P.: Critique of the fuzzball program. Phys. Rev. D 99(6), 066009 (2019). arXiv:1804.10616

  83. Bena, I., Warner, N.P.: Black holes, black rings and their microstates. Lect. Notes Phys. 755, 1–92 (2008). arXiv:hep-th/0701216

    Article  ADS  MathSciNet  MATH  Google Scholar 

  84. Breckenridge, J.C., Myers, R.C., Peet, A.W., Vafa, C.: D-branes and spinning black holes. Phys. Lett. B 391, 93–98 (1997). arXiv:hep-th/9602065

    Article  ADS  MathSciNet  MATH  Google Scholar 

  85. Bates, B., Denef, F.: Exact solutions for supersymmetric stationary black hole composites. JHEP 11, 127 (2011). arXiv:hep-th/0304094

    Article  ADS  MathSciNet  MATH  Google Scholar 

  86. Bena, I., Mayerson, D.R.: Black holes lessons from multiple ratios. arXiv:2007.09152

  87. Bena, I., Bobev, N., Giusto, S., Ruef, C., Warner, N.P.: An infinite-dimensional family of black-hole microstate geometries. JHEP 03, 022 (2011). arXiv:1006.3497, [Erratum: JHEP 04, 059 (2011)]

    Article  ADS  MathSciNet  MATH  Google Scholar 

  88. Bena, I., Shigemori, M., Warner, N.P.: Black-hole entropy from supergravity superstrata states. JHEP 10, 140 (2014). arXiv:1406.4506

    Article  ADS  MathSciNet  MATH  Google Scholar 

  89. Shigemori, M.: Counting superstrata. JHEP 10, 017 (2019). arXiv:1907.03878

    Article  ADS  MathSciNet  MATH  Google Scholar 

  90. Strominger, A., Vafa, C.: Microscopic origin of the Bekenstein–Hawking entropy. Phys. Lett. B 379, 99–104 (1996). arXiv:hep-th/9601029

    Article  ADS  MathSciNet  MATH  Google Scholar 

  91. Mayerson, D.R., Shigemori, M.: Counting D1-D5-P microstates in supergravity. arXiv:2010.04172

  92. Maldacena, J.M.: The large N limit of superconformal field theories and supergravity. Int. J. Theor. Phys. 38, 1113–1133 (1999). arXiv:hep-th/9711200

    Article  MathSciNet  MATH  Google Scholar 

  93. Kanitscheider, I., Skenderis, K., Taylor, M.: Holographic anatomy of fuzzballs. JHEP 04, 023 (2007). arXiv:hep-th/0611171

    Article  ADS  MathSciNet  Google Scholar 

  94. Kanitscheider, I., Skenderis, K., Taylor, M.: Fuzzballs with internal excitations. JHEP 06, 056 (2007). arXiv:0704.0690

    Article  ADS  MathSciNet  Google Scholar 

  95. Giusto, S., Russo, R.: Superdescendants of the D1D5 CFT and their dual 3-charge geometries. JHEP 03, 007 (2014). arXiv:1311.5536

    Article  ADS  Google Scholar 

  96. Giusto, S., Moscato, E., Russo, R.: AdS\(_{3}\) holography for 1/4 and 1/8 BPS geometries. JHEP 11, 004 (2015). arXiv:1507.00945

    Article  ADS  MATH  Google Scholar 

  97. Bena, I., Giusto, S., Russo, R., Shigemori, M., Warner, N.P.: Habemus Superstratum! A constructive proof of the existence of superstrata. JHEP 05, 110 (2015). arXiv:1503.01463

    Article  ADS  MathSciNet  MATH  Google Scholar 

  98. Heidmann, P., Warner, N.P.: Superstratum symbiosis. JHEP 09, 059 (2019). arXiv:1903.07631

    Article  ADS  MathSciNet  MATH  Google Scholar 

  99. Heidmann, P., Mayerson, D.R., Walker, R., Warner, N.P.: Holomorphic waves of black hole microstructure. JHEP 02, 192 (2020). arXiv:1910.10714

    Article  ADS  MathSciNet  MATH  Google Scholar 

  100. Mayerson, D.R., Walker, R.A., Warner, N.P.: Microstate geometries from gauged supergravity in three dimensions. arXiv:2004.13031

  101. Bena, I., Giusto, S., Martinec, E.J., Russo, R., Shigemori, M., Turton, D., Warner, N.P.: Smooth horizonless geometries deep inside the black-hole regime. Phys. Rev. Lett. 117(20), 201601 (2016). arXiv:1607.03908

  102. Tyukov, A., Walker, R., Warner, N.P.: Tidal stresses and energy gaps in microstate geometries. JHEP 02, 122 (2018). arXiv:1710.09006

    Article  ADS  MathSciNet  MATH  Google Scholar 

  103. Bena, I., Heidmann, P., Turton, D.: AdS\(_{2}\) holography: mind the cap. JHEP 12, 028 (2018). arXiv:1806.02834

    Article  ADS  MATH  Google Scholar 

  104. Shigemori, M.: Superstrata. arXiv:2002.01592

  105. Jejjala, V., Madden, O., Ross, S.F., Titchener, G.: Non-supersymmetric smooth geometries and D1-D5-P bound states. Phys. Rev. D 71, 124030 (2005). arXiv:hep-th/0504181

    Article  ADS  MathSciNet  Google Scholar 

  106. Bena, I., Giusto, S., Ruef, C., Warner, N.P.: Multi-center non-BPS black holes: the solution. JHEP 11, 032 (2009). arXiv:0908.2121

    Article  ADS  MathSciNet  Google Scholar 

  107. Bena, I., Giusto, S., Ruef, C., Warner, N.P.: A (running) bolt for new reasons. JHEP 11, 089 (2009). arXiv:0909.2559

    Article  ADS  MathSciNet  Google Scholar 

  108. Dall’Agata, G., Giusto, S., Ruef, C.: U-duality and non-BPS solutions. JHEP 02, 074 (2011). arXiv:1012.4803

    Article  ADS  MathSciNet  MATH  Google Scholar 

  109. Vasilakis, O., Warner, N.P.: Mind the gap: supersymmetry breaking in scaling. Microstate geometries. JHEP 10, 006 (2011). arXiv:1104.2641

    Article  ADS  MathSciNet  MATH  Google Scholar 

  110. Bena, I., Puhm, A., Vercnocke, B.: Metastable supertubes and non-extremal black hole microstates. JHEP 04, 100 (2012). arXiv:1109.5180

    Article  ADS  MATH  Google Scholar 

  111. Bena, I., Puhm, A., Vercnocke, B.: Non-extremal black hole microstates: fuzzballs of fire or fuzzballs of fuzz? JHEP 12, 014 (2012). arXiv:1208.3468

    Article  ADS  MathSciNet  MATH  Google Scholar 

  112. Mathur, S.D., Turton, D.: Oscillating supertubes and neutral rotating black hole microstates. JHEP 04, 072 (2014). arXiv:1310.1354

    Article  ADS  Google Scholar 

  113. Banerjee, S., Chowdhury, B.D., Vercnocke, B., Virmani, A.: Non-supersymmetric microstates of the MSW system. JHEP 05, 011 (2014). arXiv:1402.4212

    Article  ADS  Google Scholar 

  114. Bena, I., Bossard, G., Katmadas, S., Turton, D.: Non-BPS multi-bubble microstate geometries. JHEP 02, 073 (2016). arXiv:1511.03669

    Article  ADS  MathSciNet  MATH  Google Scholar 

  115. Bena, I., Bossard, G., Katmadas, S., Turton, D.: Bolting multicenter solutions. JHEP 01, 127 (2017). arXiv:1611.03500

    Article  ADS  MathSciNet  MATH  Google Scholar 

  116. Bossard, G., Katmadas, S., Turton, D.: Two kissing bolts. JHEP 02, 008 (2018). arXiv:1711.04784

    Article  ADS  MathSciNet  MATH  Google Scholar 

  117. Goldstein, K., Katmadas, S.: Almost BPS black holes. JHEP 05, 058 (2009). arXiv:0812.4183

    Article  ADS  MathSciNet  Google Scholar 

  118. Bena, I., Dall’Agata, G., Giusto, S., Ruef, C., Warner, N.P.: Non-BPS black rings and black holes in Taub-NUT. JHEP 06, 015 (2009). arXiv:0902.4526

    Article  ADS  MathSciNet  Google Scholar 

  119. Bena, I., Guica, M., Song, W.: Un-twisting the NHEK with spectral flows. JHEP 03, 028 (2013). arXiv:1203.4227

    Article  ADS  MathSciNet  MATH  Google Scholar 

  120. Bena, I., Bobev, N., Warner, N.P.: Spectral flow, and the spectrum of multi-center solutions. Phys. Rev. D 77, 125025 (2008). arXiv:0803.1203

    Article  ADS  MathSciNet  Google Scholar 

  121. Heidmann, P.: Bubbling the NHEK. JHEP 01, 108 (2019). arXiv:1811.08256

    Article  ADS  MathSciNet  MATH  Google Scholar 

  122. Policastro, G., Son, D.T., Starinets, A.O.: The shear viscosity of strongly coupled \(N=4\) supersymmetric Yang–Mills plasma. Phys. Rev. Lett. 87, 081601 (2001). arXiv:hep-th/0104066

    Article  ADS  Google Scholar 

  123. Son, D.T., Starinets, A.O.: Viscosity, black holes, and quantum field theory. Ann. Rev. Nucl. Part. Sci. 57, 95–118 (2007). arXiv:0704.0240

    Article  ADS  Google Scholar 

  124. Cremonini, S.: The shear viscosity to entropy ratio: a status report. Mod. Phys. Lett. B 25, 1867–1888 (2011). arXiv:1108.0677

    Article  ADS  MathSciNet  MATH  Google Scholar 

  125. Shuryak, E.V.: What RHIC experiments and theory tell us about properties of quark–gluon plasma? Nucl. Phys. A 750, 64–83 (2005). arXiv:hep-ph/0405066

    Article  ADS  Google Scholar 

  126. Bena, I., Mayerson, D.R., Puhm, A., Vercnocke, B.: Tunneling into microstate geometries: quantum effects stop gravitational collapse. JHEP 07, 031 (2016). arXiv:1512.05376

    Article  ADS  MathSciNet  MATH  Google Scholar 

  127. Charles, A.M., Mayerson, D.R.: Probing black hole microstate evolution with networks and random walks. SciPost Phys. 8(5), 077 (2020). arXiv:1812.09328

  128. Addazi, A., Bianchi, M., Firrotta, M., Marcianò, A.: String memories ... lost and regained. arXiv:2008.02206

  129. Addazi, A., Bianchi, M., Veneziano, G.: Glimpses of black hole formation/evaporation in highly inelastic, ultra-planckian string collisions. JHEP 02, 111 (2017). arXiv:1611.03643

    Article  ADS  MathSciNet  MATH  Google Scholar 

  130. Lunin, O., Mathur, S.D.: AdS/CFT duality and the black hole information paradox. Nucl. Phys. B 623, 342–394 (2002). arXiv:hep-th/0109154

    Article  ADS  MathSciNet  MATH  Google Scholar 

  131. Lunin, O., Maldacena, J.M., Maoz, L.: Gravity solutions for the D1–D5 system with angular momentum. arXiv:hep-th/0212210

  132. Rychkov, V.S.: D1–D5 black hole microstate counting from supergravity. JHEP 01, 063 (2006). arXiv:hep-th/0512053

    Article  ADS  MathSciNet  Google Scholar 

  133. Krishnan, C., Raju, A.: A note on D1–D5 entropy and geometric quantization. JHEP 06, 054 (2015). arXiv:1504.04330

    Article  ADS  MathSciNet  MATH  Google Scholar 

  134. Lunin, O., Mathur, S.D.: Statistical interpretation of Bekenstein entropy for systems with a stretched horizon. Phys. Rev. Lett. 88, 211303 (2002). arXiv:hep-th/0202072

    Article  ADS  MathSciNet  MATH  Google Scholar 

  135. de Boer, J., El-Showk, S., Messamah, I., Van den Bleeken, D.: A Bound on the entropy of supergravity? JHEP 02, 062 (2010). arXiv:0906.0011

    Article  MathSciNet  MATH  Google Scholar 

  136. Balasubramanian, V., Czech, B., Hubeny, V.E., Larjo, K., Rangamani, M., Simon, J.: Typicality versus thermality: an analytic distinction. Gen. Rel. Grav. 40, 1863–1890 (2008). arXiv:hep-th/0701122

    Article  ADS  MathSciNet  MATH  Google Scholar 

  137. Bao, N., Ooguri, H.: Distinguishability of black hole microstates. Phys. Rev. D 96(6), 066017 (2017). arXiv:1705.07943

  138. Michel, B., Puhm, A.: Corrections in the relative entropy of black hole microstates. JHEP 07, 179 (2018). arXiv:1801.02615

    Article  ADS  MathSciNet  MATH  Google Scholar 

  139. Guo, W.-Z., Lin, F.-L., Zhang, J.: Distinguishing black hole microstates using Holevo information. Phys. Rev. Lett. 121(25), 251603 (2018). arXiv:1808.02873

  140. Bena, I., Wang, C.-W., Warner, N.P.: Plumbing the Abyss: black ring microstates. JHEP 07, 019 (2008). arXiv:0706.3786

    Article  ADS  MathSciNet  Google Scholar 

  141. de Boer, J., El-Showk, S., Messamah, I., Van den Bleeken, D.: Quantizing \(N=2\) multicenter solutions. JHEP 05, 002 (2009). arXiv:0807.4556

    Article  MathSciNet  Google Scholar 

  142. Hertog, T., Hartle, J.: Observational implications of fuzzball formation. Gen. Rel. Grav. 52(7), 67 (2020). arXiv:1704.02123

  143. Cardoso, V., Franzin, E., Pani, P.: Is the gravitational-wave ringdown a probe of the event horizon? Phys. Rev. Lett. 116(17), 171101 (2016). arXiv:1602.07309, [Erratum: Phys.Rev.Lett. 117, 089902 (2016)]

  144. V. Cardoso, S. Hopper, C. F. B. Macedo, C. Palenzuela and P. Pani, Gravitational-wave signatures of exotic compact objects and of quantum corrections at the horizon scale, Phys. Rev. D 94 (2016), no. 8, 084031, arXiv:1608.08637

  145. Bueno, P., Cano, P.A., Goelen, F., Hertog, T., Vercnocke, B.: Echoes of Kerr-like wormholes. Phys. Rev. D 97(2), 024040 (2018). arXiv:1711.00391

  146. Testa, A., Pani, P.: Analytical template for gravitational-wave echoes: signal characterization and prospects of detection with current and future interferometers. Phys. Rev. D 98(4), 044018 (2018). arXiv:1806.04253

  147. DarkGRA: Catalogue of gravitational-wave echo waveforms. https://www.darkgra.org/gw-echo-catalogue.html Accessed 12 October 2020

  148. Testa, A.: Master Thesis, Sapienza University of Rome (2018)

  149. Mark, Z., Zimmerman, A., Du, S.M., Chen, Y.: A recipe for echoes from exotic compact objects. Phys. Rev. D 96(8), 084002 (2017). arXiv:1706.06155

  150. Bena, I., Heidmann, P., Monten, R., Warner, N.P.: Thermal decay without information loss in horizonless microstate geometries. SciPost Phys. 7(5), 063 (2019). arXiv:1905.05194

  151. Hui, L., Kabat, D., Wong, S.S.: Quasinormal modes, echoes and the causal structure of the Green’s function. JCAP 12, 020 (2019). arXiv:1909.10382

    Article  ADS  Google Scholar 

  152. Abedi, J., Dykaar, H., Afshordi, N.: Echoes from the Abyss: tentative evidence for Planck-scale structure at black hole horizons. Phys. Rev. D 96(8), 082004 (2017). arXiv:1612.00266

  153. Ashton, G., Birnholtz, O., Cabero, M., Capano, C., Dent, T., Krishnan, B., Meadors, G.D., Nielsen, A.B., Nitz, A., Westerweck, J.: Comments on: ”Echoes from the abyss: Evidence for Planck-scale structure at black hole horizons”. arXiv:1612.05625

  154. Martinec, E.J., Warner, N.P.: The harder they fall, the bigger they become: tidal trapping of strings by microstate geometries. arXiv:2009.07847

  155. Avery, S.G., Chowdhury, B.D., Mathur, S.D.: Emission from the D1D5 CFT. JHEP 10, 065 (2009). arXiv:0906.2015

    Article  ADS  Google Scholar 

  156. Chakrabarty, B., Turton, D., Virmani, A.: Holographic description of non-supersymmetric orbifolded D1–D5–P solutions. JHEP 11, 063 (2015). arXiv:1508.01231

    Article  ADS  MathSciNet  MATH  Google Scholar 

  157. Chakrabarty, B., Ghosh, D., Virmani, A.: Quasinormal modes of supersymmetric microstate geometries from the D1–D5 CFT. JHEP 10, 072 (2019). arXiv:1908.01461

    Article  ADS  MathSciNet  MATH  Google Scholar 

  158. Bena, I., Eperon, F., Heidmann, P., Warner, N.P.: The great escape: tunneling out of microstate geometries. arXiv:2005.11323

  159. Geroch, R.P.: Multipole moments. II. Curved space. J. Math. Phys. 11, 2580–2588 (1970)

  160. Hansen, R.: Multipole moments of stationary space–times. J. Math. Phys. 15, 46–52 (1974)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  161. Thorne, K.S.: Multipole expansions of gravitational radiation. Rev. Mod. Phys. 52, 299–339 (1980)

    Article  ADS  MathSciNet  Google Scholar 

  162. Cardoso, V., Gualtieri, L.: Testing the black hole ’no-hair’ hypothesis. Class. Quant. Grav. 33(17), 174001 (2016). arXiv:1607.03133

  163. Sotiriou, T.P., Apostolatos, T.A.: Corrected multipole moments of axisymmetric electrovacuum spacetimes. Class. Quant. Grav. 21, 5727–5733 (2004). arXiv:gr-qc/0407064

    Article  ADS  MATH  Google Scholar 

  164. Ryan, F.D.: Effect of gravitational radiation reaction on circular orbits around a spinning black hole. Phys. Rev. D 52, 3159–3162 (1995). arXiv:gr-qc/9506023

    Article  ADS  Google Scholar 

  165. Bena, I., Mayerson, D.R.: A new window into black holes. arXiv:2006.10750

  166. Bianchi, M., Consoli, D., Grillo, A., Morales, J.F., Pani, P., Raposo, G.: Distinguishing fuzzballs from black holes through their multipolar structure. arXiv:2007.01743

  167. Bianchi, M., Consoli, D., Grillo, A., Morales, J.F., Pani, P., Raposo, G.: The multipolar structure of fuzzballs. arXiv:2008.01445

  168. Bah, I., Bena, I., Heidmann, P., Li, Y., Mayerson, D.R.: Multipole moments of almost-BPS geometries (in press)

  169. Cardoso, V., Franzin, E., Maselli, A., Pani, P., Raposo, G.: Testing strong-field gravity with tidal love numbers. Phys. Rev. D 95(8), 084014 (2017). arXiv:1701.01116, [Addendum: Phys. Rev. D 95, 089901 (2017)]

  170. Pani, P., Maselli, A.: Love in extrema ratio. Int. J. Mod. Phys. D 28(14), 1944001 (2019). arXiv:1905.03947

  171. Kol, B., Smolkin, M.: Black hole stereotyping: induced gravito-static polarization. JHEP 02, 010 (2012). arXiv:1110.3764

    Article  ADS  MATH  Google Scholar 

  172. Pani, P., Gualtieri, L., Abdelsalhin, T., Jiménez-Forteza, X.: Magnetic tidal love numbers clarified. Phys. Rev. D 98(12), 124023 (2018). arXiv:1810.01094

  173. Damour, T., Nagar, A.: Relativistic tidal properties of neutron stars. Phys. Rev. D 80, 084035 (2009). arXiv:0906.0096

    Article  ADS  Google Scholar 

  174. Binnington, T., Poisson, E.: Relativistic theory of tidal Love numbers. Phys. Rev. D 80, 084018 (2009). arXiv:0906.1366

    Article  ADS  Google Scholar 

  175. Gürlebeck, N.: No-hair theorem for black holes in astrophysical environments. Phys. Rev. Lett. 114(15), 151102 (2015). arXiv:1503.03240

  176. Landry, P., Poisson, E.: Tidal deformation of a slowly rotating material body. External metric. Phys. Rev. D 91, 104018 (2015). arXiv:1503.07366

  177. Pani, P., Gualtieri, L., Maselli, A., Ferrari, V.: Tidal deformations of a spinning compact object. Phys. Rev. D 92(2), 024010 (2015). arXiv:1503.07365

  178. Le Tiec, A., Casals, M.: Spinning black holes fall in love. arXiv:2007.00214

  179. Chia, H.S.: Tidal deformation and dissipation of rotating black holes. arXiv:2010.07300

  180. Cardoso, V., Kimura, M., Maselli, A., Senatore, L. : Black holes in an effective field theory extension of general relativity. Phys. Rev. Lett. 121(25), 251105 (2018). arXiv:1808.08962

  181. Brustein, R., Sherf, Y.: Quantum love. arXiv:2008.02738

  182. Hui, L., Joyce, A., Penco, R., Santoni, L., Solomon, A.R.: Static response and Love numbers of Schwarzschild black holes. arXiv:2010.00593

  183. Bena, I., Heidmann, P., Mayerson, D.R.: Tidal love numbers for microstate geometries (in press)

  184. Bacchini, F., Davelaar, J., Hertog, T., Mayerson, D.R., Olivares, H., Ripperda , B., Vercnocke, B.: Shadows of four-dimensional fuzzballs (in press)

  185. Kuchler, L., Lemmens, T., Vercnocke, B.: Imaging five-dimensional microstate geometries (in press)

  186. Hertog, T., Lemmens, T., Vercnocke, B.: Imaging higher dimensional black objects. Phys. Rev. D 100(4), 046011 (2019). arXiv:1903.05125

  187. Ahmed, F., Singh, D.V., Ghosh, S.G.: 5D rotating regular Myers–Perry black holes and their shadow. arXiv:2008.10241

  188. Belhaj, A., Belmahi, H., Benali, M., Hadri, W.E., El Moumni, H., Torrente-Lujan, E.: Shadows of 5D black holes from string theory. arXiv:2008.13478

  189. Bena, I., Turton, D., Walker, R., Warner, N.P.: Integrability and black-hole microstate geometries. JHEP 11, 021 (2017). arXiv:1709.01107

    Article  ADS  MathSciNet  MATH  Google Scholar 

  190. Walker, R.: D1–D5–P superstrata in 5 and 6 dimensions: separable wave equations and prepotentials. JHEP 09, 117 (2019). arXiv:1906.04200

    Article  ADS  MathSciNet  MATH  Google Scholar 

  191. Bianchi, M., Consoli, D., Grillo, A., Morales, J.F.: The dark side of fuzzball geometries. JHEP 05, 126 (2019). arXiv:1811.02397

    Article  ADS  MathSciNet  MATH  Google Scholar 

  192. Bianchi, M., Consoli, D., Morales, J.: Probing fuzzballs with particles. Waves and strings. JHEP 06, 157 (2018). arXiv:1711.10287

    Article  ADS  MathSciNet  MATH  Google Scholar 

  193. Eperon, F.C., Reall, H.S., Santos, J.E.: Instability of supersymmetric microstate geometries. JHEP 10, 031 (2016). arXiv:1607.06828

    Article  ADS  MathSciNet  MATH  Google Scholar 

  194. Keir, J.: Wave propagation on microstate geometries. Ann. Henri Poinc. 21(3), 705–760 (2019). arXiv:1609.01733

  195. Eperon, F.C.: Geodesics in supersymmetric microstate geometries. Class. Quant. Grav. 34(16), 165003 (2017). arXiv:1702.03975

  196. Bianchi, M., Casolino, M., Rizzo, G.: Accelerating strangelets via Penrose process in non-BPS fuzzballs. Nucl. Phys. B 954, 115010 (2020). arXiv:1904.01097

    Article  Google Scholar 

  197. Cardoso, V., Dias, O.J., Hovdebo, J.L., Myers, R.C.: Instability of non-supersymmetric smooth geometries. Phys. Rev. D 73, 064031 (2006). arXiv:hep-th/0512277

    Article  ADS  MathSciNet  Google Scholar 

  198. Marolf, D., Michel, B., Puhm, A.: A rough end for smooth microstate geometries. JHEP 05, 021 (2017). arXiv:1612.05235

    Article  ADS  MathSciNet  MATH  Google Scholar 

  199. Bena, I., Martinec, E.J., Walker, R., Warner, N.P.: Early scrambling and capped BTZ geometries. JHEP 04, 126 (2019). arXiv:1812.05110

    Article  ADS  MathSciNet  MATH  Google Scholar 

  200. Bena, I., Houppe, A., Warner, N.P.: Delaying the inevitable: tidal disruption in microstate geometries. arXiv:2006.13939

  201. Craps, B., De Clerck, M., Hacker, P., Nguyen, K., Rabideau, C.: Slow scrambling in extremal BTZ and microstate geometries. arXiv:2009.08518

  202. Polchinski, J.: Chaos in the black hole S-matrix. arXiv:1505.08108

  203. Maldacena, J., Shenker, S.H., Stanford, D.: A bound on chaos. JHEP 08, 106 (2016). arXiv:1503.01409

    Article  ADS  MathSciNet  MATH  Google Scholar 

  204. Hampton, S., Mathur, S.D.: Thermalization in the D1D5 CFT. JHEP 06, 004 (2020). arXiv:1910.01690

    Article  ADS  MathSciNet  MATH  Google Scholar 

  205. 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). arXiv:0812.1806

    Article  ADS  MathSciNet  Google Scholar 

  206. Bianchi, M., Grillo, A., Morales, J.F.: Chaos at the rim of black hole and fuzzball shadows. JHEP 05, 078 (2020). arXiv:2002.05574

    Article  ADS  MathSciNet  Google Scholar 

  207. Asali, Y., Pang, P.T., Samajdar, A., Van Den Broeck, C.: Probing resonant excitations in exotic compact objects via gravitational waves. Phys. Rev. D 102(2), 024016 (2020). arXiv:2004.05128

  208. Fransen, K., Koekoek, G., Tielemans, R., Vercnocke, B.: Modeling and detecting resonant tides of exotic compact objects. arXiv:2005.12286

  209. Datta, S., Bose, S.: Probing the nature of central objects in extreme-mass-ratio inspirals with gravitational waves. Phys. Rev. D 99(8), 084001 (2019).arXiv:1902.01723

  210. Datta, S., Brito, R., Bose, S., Pani, P., Hughes, S.A.: Tidal heating as a discriminator for horizons in extreme mass ratio inspirals. Phys. Rev. D 101(4), 044004 (2020). arXiv:1910.07841

  211. Datta, S., Phukon, K.S., Bose, S.: Recognizing black holes in gravitational-wave observations: telling apart impostors in mass-gap binaries. arXiv:2004.05974

  212. Datta, S.: Tidal heating of quantum black holes and their imprints on gravitational waves. Phys. Rev. D 102(6), 064040 (2020). arXiv:2002.04480

  213. Macedo, C.F., Pani, P., Cardoso, V., Crispino, L.C.B.: Astrophysical signatures of boson stars: quasinormal modes and inspiral resonances. Phys. Rev. D 88(6), 064046 (2013). arXiv:1307.4812

  214. Macedo, C.F., Pani, P., Cardoso, V., Crispino, L.C.: Into the lair: gravitational-wave signatures of dark matter. Astrophys. J. 774, 48 (2013). arXiv:1302.2646

    Article  ADS  Google Scholar 

  215. Barausse, E., et al.: Prospects for fundamental physics with LISA. Gen. Rel. Grav. 52(8), 81 (2020). arXiv:2001.09793

  216. Cunha, P.V.P., Herdeiro, C.A.R., Radu, E., Runarsson, H.F.: Shadows of Kerr black holes with scalar hair. Phys. Rev. Lett. 115(21), 211102 (2015). arXiv:1509.00021

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Acknowledgements

I would like to thank the editors of the General Relativity and Gravitation Topical Collection on The Fuzzball Paradigm for the invitation to contribute this review. I would also like to thank I. Bena, B. Ripperda, D. Turton, B. Vercnocke, A. Virmani, R. Walker, and N. Warner for many insightful and interesting discussions, as well as suggestions and comments on this paper. I am especially grateful to B. Vercnocke for introducing me to this research avenue and for many enthousiastic discussions over the years. I am supported by ERC Advanced Grant 787320 - QBH Structure and ERC Starting Grant 679278 - Emergent-BH.

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    Daniel R. Mayerson

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Mayerson, D.R. Fuzzballs and observations. Gen Relativ Gravit 52, 115 (2020). https://doi.org/10.1007/s10714-020-02769-w

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