Advertisement

Journal of High Energy Physics

, 2019:215 | Cite as

Compact objects and the swampland

  • Carlos A. R. Herdeiro
  • Eugen Radu
  • Kunihito UzawaEmail author
Open Access
Regular Article - Theoretical Physics
  • 22 Downloads

Abstract

Recently, two simple criteria were proposed to assess if vacua emerging from an effective scalar field theory are part of the string “landscape” or “swampland”. The former are the vacua that emerge from string compactifications; the latter are not obtained by any such compactification and hence may not survive in a UV completed theory of gravity. So far, these criteria have been applied to inflationary and dark energy models. Here we consider them in the context of solitonic compact objects made up of scalar fields: boson stars. Analysing several models (static, rotating, with and without self-interactions), we find that, in this context, the criteria are not independent. Furthermore, we find the universal behaviour that in the region wherein the boson stars are expected to be perturbatively stable, the compact objects may be part of the landscape. By contrast, in the region where they may be faithful black hole mimickers, in the sense they possess a light ring, the criteria fail (are obeyed) for static (rotating) ultracompact boson stars, which should thus be part of the swampland (landscape). We also consider hairy black holes interpolating between these boson stars and the Kerr solution and establish the part of the domain of existence where the swampland criteria are violated. In interpreting these results one should bear in mind, however, that the swampland criteria are not quantitatively strict.

Keywords

Classical Theories of Gravity Black Holes Superstring Vacua 

Notes

Open Access

This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.

References

  1. [1]
    Supernova Search Team collaboration, Observational evidence from supernovae for an accelerating universe and a cosmological constant, Astron. J. 116 (1998) 1009 [astro-ph/9805201] [INSPIRE].
  2. [2]
    S. Perlmutter, M.S. Turner and M.J. White, Constraining dark energy with SNe Ia and large scale structure, Phys. Rev. Lett. 83 (1999) 670 [astro-ph/9901052] [INSPIRE].
  3. [3]
    WMAP collaboration, Nine-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Final Maps and Results, Astrophys. J. Suppl. 208 (2013) 20 [arXiv:1212.5225] [INSPIRE].
  4. [4]
    Planck collaboration, Planck 2013 results. XVI. Cosmological parameters, Astron. Astrophys. 571 (2014) A16 [arXiv:1303.5076] [INSPIRE].
  5. [5]
    C. Blake and K. Glazebrook, Probing dark energy using baryonic oscillations in the galaxy power spectrum as a cosmological ruler, Astrophys. J. 594 (2003) 665 [astro-ph/0301632] [INSPIRE].
  6. [6]
    H.-J. Seo and D.J. Eisenstein, Probing dark energy with baryonic acoustic oscillations from future large galaxy redshift surveys, Astrophys. J. 598 (2003) 720 [astro-ph/0307460] [INSPIRE].
  7. [7]
    S.D.M. White, J.F. Navarro, A.E. Evrard and C.S. Frenk, The baryon content of galaxy clusters: A challenge to cosmological orthodoxy, Nature 366 (1993) 429 [INSPIRE].ADSCrossRefGoogle Scholar
  8. [8]
    P. Schuecker, H. Bohringer, C.A. Collins and L. Guzzo, The REFLEX galaxy cluster survey VII: Ωm and σ 8 from cluster abundance and large scale clustering, Astron. Astrophys. 398 (2003) 867 [astro-ph/0208251] [INSPIRE].
  9. [9]
    M. Kilbinger et al., Dark energy constraints and correlations with systematics from CFHTLS weak lensing, SNLS supernovae Ia and WMAP5, Astron. Astrophys. 497 (2009) 677 [arXiv:0810.5129] [INSPIRE].ADSCrossRefGoogle Scholar
  10. [10]
    D.M. Scolnic et al., The Complete Light-curve Sample of Spectroscopically Confirmed SNe Ia from Pan-STARRS1 and Cosmological Constraints from the Combined Pantheon Sample, Astrophys. J. 859 (2018) 101 [arXiv:1710.00845] [INSPIRE].ADSCrossRefGoogle Scholar
  11. [11]
    Planck collaboration, Planck 2018 results. VI. Cosmological parameters, arXiv:1807.06209 [INSPIRE].
  12. [12]
    BICEP2 and Keck Array collaborations, BICEP2/Keck Array V: Measurements of B-mode Polarization at Degree Angular Scales and 150 GHz by the Keck Array, Astrophys. J. 811 (2015) 126 [arXiv:1502.00643] [INSPIRE].
  13. [13]
    M. Graña, Flux compactifications in string theory: A comprehensive review, Phys. Rept. 423 (2006) 91 [hep-th/0509003] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  14. [14]
    M.R. Douglas and S. Kachru, Flux compactification, Rev. Mod. Phys. 79 (2007) 733 [hep-th/0610102] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  15. [15]
    R. Blumenhagen, B. Körs, D. Lüst and S. Stieberger, Four-dimensional String Compactifications with D-branes, Orientifolds and Fluxes, Phys. Rept. 445 (2007) 1 [hep-th/0610327] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  16. [16]
    S. Gukov, C. Vafa and E. Witten, CFT’s from Calabi-Yau four folds, Nucl. Phys. B 584 (2000) 69 [Erratum ibid. B 608 (2001) 477] [hep-th/9906070] [INSPIRE].
  17. [17]
    S.B. Giddings, S. Kachru and J. Polchinski, Hierarchies from fluxes in string compactifications, Phys. Rev. D 66 (2002) 106006 [hep-th/0105097] [INSPIRE].ADSMathSciNetGoogle Scholar
  18. [18]
    S. Kachru, M.B. Schulz and S. Trivedi, Moduli stabilization from fluxes in a simple IIB orientifold, JHEP 10 (2003) 007 [hep-th/0201028] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  19. [19]
    S. Kachru, R. Kallosh, A.D. Linde and S.P. Trivedi, de Sitter vacua in string theory, Phys. Rev. D 68 (2003) 046005 [hep-th/0301240] [INSPIRE].
  20. [20]
    S. Kachru, R. Kallosh, A.D. Linde, J.M. Maldacena, L.P. McAllister and S.P. Trivedi, Towards inflation in string theory, JCAP 10 (2003) 013 [hep-th/0308055] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  21. [21]
    V. Balasubramanian, P. Berglund, J.P. Conlon and F. Quevedo, Systematics of moduli stabilisation in Calabi-Yau flux compactifications, JHEP 03 (2005) 007 [hep-th/0502058] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  22. [22]
    H. Kodama and K. Uzawa, Moduli instability in warped compactifications of the type IIB supergravity, JHEP 07 (2005) 061 [hep-th/0504193] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  23. [23]
    O. DeWolfe, A. Giryavets, S. Kachru and W. Taylor, Type IIA moduli stabilization, JHEP 07 (2005) 066 [hep-th/0505160] [INSPIRE].ADSMathSciNetGoogle Scholar
  24. [24]
    H. Kodama and K. Uzawa, Comments on the four-dimensional effective theory for warped compactification, JHEP 03 (2006) 053 [hep-th/0512104] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  25. [25]
    B. de Wit, D.J. Smit and N.D. Hari Dass, Residual Supersymmetry of Compactified D = 10 Supergravity, Nucl. Phys. B 283 (1987) 165 [INSPIRE].ADSCrossRefGoogle Scholar
  26. [26]
    J.M. Maldacena and C. Núñez, Supergravity description of field theories on curved manifolds and a no go theorem, Int. J. Mod. Phys. A 16 (2001) 822 [hep-th/0007018] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  27. [27]
    S. Ivanov and G. Papadopoulos, A no go theorem for string warped compactifications, Phys. Lett. B 497 (2001) 309 [hep-th/0008232] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  28. [28]
    N. Goheer, M. Kleban and L. Susskind, The trouble with de Sitter space, JHEP 07 (2003) 056 [hep-th/0212209] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  29. [29]
    M.P. Hertzberg, S. Kachru, W. Taylor and M. Tegmark, Inflationary Constraints on Type IIA String Theory, JHEP 12 (2007) 095 [arXiv:0711.2512] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  30. [30]
    U.H. Danielsson and T. Van Riet, What if string theory has no de Sitter vacua?, Int. J. Mod. Phys. D 27 (2018) 1830007 [arXiv:1804.01120] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  31. [31]
    L. Susskind, The anthropic landscape of string theory, hep-th/0302219 [INSPIRE].
  32. [32]
    T. Banks, M. Dine and E. Gorbatov, Is there a string theory landscape?, JHEP 08 (2004) 058 [hep-th/0309170] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  33. [33]
    F. Denef and M.R. Douglas, Distributions of flux vacua, JHEP 05 (2004) 072 [hep-th/0404116] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  34. [34]
    R. Kallosh and A.D. Linde, Landscape, the scale of SUSY breaking and inflation, JHEP 12 (2004) 004 [hep-th/0411011] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  35. [35]
    C. Vafa, The string landscape and the swampland, hep-th/0509212 [INSPIRE].
  36. [36]
    F. Denef, Les Houches Lectures on Constructing String Vacua, Les Houches 87 (2008) 483 [arXiv:0803.1194] [INSPIRE].CrossRefGoogle Scholar
  37. [37]
    T.D. Brennan, F. Carta and C. Vafa, The String Landscape, the Swampland and the Missing Corner, PoS(TASI2017)015 (2017) [arXiv:1711.00864] [INSPIRE].
  38. [38]
    H. Ooguri and C. Vafa, On the Geometry of the String Landscape and the Swampland, Nucl. Phys. B 766 (2007) 21 [hep-th/0605264] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  39. [39]
    H. Ooguri and C. Vafa, Non-supersymmetric AdS and the Swampland, Adv. Theor. Math. Phys. 21 (2017) 1787 [arXiv:1610.01533] [INSPIRE].MathSciNetCrossRefzbMATHGoogle Scholar
  40. [40]
    G. Obied, H. Ooguri, L. Spodyneiko and C. Vafa, de Sitter Space and the Swampland, arXiv:1806.08362 [INSPIRE].
  41. [41]
    P. Agrawal, G. Obied, P.J. Steinhardt and C. Vafa, On the Cosmological Implications of the String Swampland, Phys. Lett. B 784 (2018) 271 [arXiv:1806.09718] [INSPIRE].ADSCrossRefGoogle Scholar
  42. [42]
    H. Ooguri, E. Palti, G. Shiu and C. Vafa, Distance and de Sitter Conjectures on the Swampland, Phys. Lett. B 788 (2019) 180 [arXiv:1810.05506] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  43. [43]
    J. Brown, W. Cottrell, G. Shiu and P. Soler, Fencing in the Swampland: Quantum Gravity Constraints on Large Field Inflation, JHEP 10 (2015) 023 [arXiv:1503.04783] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  44. [44]
    R. Blumenhagen, I. Valenzuela and F. Wolf, The Swampland Conjecture and F-term Axion Monodromy Inflation, JHEP 07 (2017) 145 [arXiv:1703.05776] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  45. [45]
    A. Achúcarro and G.A. Palma, The string swampland constraints require multi-field inflation, arXiv:1807.04390 [INSPIRE].
  46. [46]
    S.K. Garg and C. Krishnan, Bounds on Slow Roll and the de Sitter Swampland, arXiv:1807.05193 [INSPIRE].
  47. [47]
    A. Kehagias and A. Riotto, A note on Inflation and the Swampland, Fortsch. Phys. 66 (2018) 100052 [arXiv:1807.05445] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  48. [48]
    H. Matsui and F. Takahashi, Eternal Inflation and Swampland Conjectures, arXiv:1807.11938 [INSPIRE].
  49. [49]
    C. Damian and O. Loaiza-Brito, Two-field axion inflation and the swampland constraint in the flux-scaling scenario, arXiv:1808.03397 [INSPIRE].
  50. [50]
    W.H. Kinney, S. Vagnozzi and L. Visinelli, The Zoo Plot Meets the Swampland: Mutual (In)Consistency of Single-Field Inflation, String Conjectures and Cosmological Data, arXiv:1808.06424 [INSPIRE].
  51. [51]
    S. Brahma and M. Wali Hossain, Avoiding the string swampland in single-field inflation: Excited initial states, arXiv:1809.01277 [INSPIRE].
  52. [52]
    C. Han, S. Pi and M. Sasaki, Quintessence Saves Higgs Instability, arXiv:1809.05507 [INSPIRE].
  53. [53]
    K. Dimopoulos, Steep Eternal Inflation and the Swampland, Phys. Rev. D 98 (2018) 123516 [arXiv:1810.03438] [INSPIRE].ADSGoogle Scholar
  54. [54]
    C.-M. Lin, K.-W. Ng and K. Cheung, Chaotic inflation on the brane and the Swampland Criteria, arXiv:1810.01644 [INSPIRE].
  55. [55]
    A. Ashoorioon, Rescuing Single Field Inflation from the Swampland, arXiv:1810.04001 [INSPIRE].
  56. [56]
    S. Das, Warm Inflation in the light of Swampland Criteria, arXiv:1810.05038 [INSPIRE].
  57. [57]
    S.-J. Wang, Quintessential Starobinsky inflation and swampland criteria, arXiv:1810.06445 [INSPIRE].
  58. [58]
    S.K. Garg, C. Krishnan and M. Zaid, Bounds on Slow Roll at the Boundary of the Landscape, arXiv:1810.09406 [INSPIRE].
  59. [59]
    J.J. Heckman, C. Lawrie, L. Lin and G. Zoccarato, F-theory and Dark Energy, arXiv:1811.01959 [INSPIRE].
  60. [60]
    C.-I. Chiang, J.M. Leedom and H. Murayama, What does Inflation say about Dark Energy given the Swampland Conjectures?, arXiv:1811.01987 [INSPIRE].
  61. [61]
    F.E. Schunck and E.W. Mielke, General relativistic boson stars, Class. Quant. Grav. 20 (2003) R301 [arXiv:0801.0307] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  62. [62]
    S.L. Liebling and C. Palenzuela, Dynamical Boson Stars, Living Rev. Rel. 15 (2012) 6 [arXiv:1202.5809] [INSPIRE].CrossRefzbMATHGoogle Scholar
  63. [63]
    D.J. Kaup, Klein-Gordon Geon, Phys. Rev. 172 (1968) 1331 [INSPIRE].ADSCrossRefGoogle Scholar
  64. [64]
    R. Ruffini and S. Bonazzola, Systems of selfgravitating particles in general relativity and the concept of an equation of state, Phys. Rev. 187 (1969) 1767 [INSPIRE].ADSCrossRefGoogle Scholar
  65. [65]
    E. Seidel and W.-M. Suen, Formation of solitonic stars through gravitational cooling, Phys. Rev. Lett. 72 (1994) 2516 [gr-qc/9309015] [INSPIRE].
  66. [66]
    P. Jetzer, Dynamical Instability of Bosonic Stellar Configurations, Nucl. Phys. B 316 (1989) 411 [INSPIRE].ADSCrossRefGoogle Scholar
  67. [67]
    M. Gleiser and R. Watkins, Gravitational Stability of Scalar Matter, Nucl. Phys. B 319 (1989) 733 [INSPIRE].ADSCrossRefGoogle Scholar
  68. [68]
    T.D. Lee and Y. Pang, Stability of Mini-Boson Stars, Nucl. Phys. B 315 (1989) 477 [INSPIRE].ADSCrossRefGoogle Scholar
  69. [69]
    F.S. Guzman and J.M. Rueda-Becerril, Spherical boson stars as black hole mimickers, Phys. Rev. D 80 (2009) 084023 [arXiv:1009.1250] [INSPIRE].ADSGoogle Scholar
  70. [70]
    F.H. Vincent, Z. Meliani, P. Grandclement, E. Gourgoulhon and O. Straub, Imaging a boson star at the Galactic center, Class. Quant. Grav. 33 (2016) 105015 [arXiv:1510.04170] [INSPIRE].ADSCrossRefGoogle Scholar
  71. [71]
    P.V.P. Cunha, J.A. Font, C. Herdeiro, E. Radu, N. Sanchis-Gual and M. Zilhão, Lensing and dynamics of ultracompact bosonic stars, Phys. Rev. D 96 (2017) 104040 [arXiv:1709.06118] [INSPIRE].ADSGoogle Scholar
  72. [72]
    A. Suárez, V.H. Robles and T. Matos, A Review on the Scalar Field/Bose-Einstein Condensate Dark Matter Model, Astrophys. Space Sci. Proc. 38 (2014) 107 [arXiv:1302.0903] [INSPIRE].ADSCrossRefGoogle Scholar
  73. [73]
    S. Krippendorf, F. Muia and F. Quevedo, Moduli Stars, JHEP 08 (2018) 070 [arXiv:1806.04690] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  74. [74]
    B. Li, T. Rindler-Daller and P.R. Shapiro, Cosmological Constraints on Bose-Einstein-Condensed Scalar Field Dark Matter, Phys. Rev. D 89 (2014) 083536 [arXiv:1310.6061] [INSPIRE].ADSGoogle Scholar
  75. [75]
    F.E. Schunck and E.W. Mielke, Rotating boson star as an effective mass torus in general relativity, Phys. Lett. A 249 (1998) 389 [INSPIRE].ADSCrossRefGoogle Scholar
  76. [76]
    S. Yoshida and Y. Eriguchi, Rotating boson stars in general relativity, Phys. Rev. D 56 (1997) 762 [INSPIRE].ADSMathSciNetGoogle Scholar
  77. [77]
    C.A.R. Herdeiro and E. Radu, Kerr black holes with scalar hair, Phys. Rev. Lett. 112 (2014) 221101 [arXiv:1403.2757] [INSPIRE].ADSCrossRefGoogle Scholar
  78. [78]
    C. Herdeiro and E. Radu, Construction and physical properties of Kerr black holes with scalar hair, Class. Quant. Grav. 32 (2015) 144001 [arXiv:1501.04319] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  79. [79]
    R.P. Kerr, Gravitational field of a spinning mass as an example of algebraically special metrics, Phys. Rev. Lett. 11 (1963) 237 [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  80. [80]
    M. Colpi, S.L. Shapiro and I. Wasserman, Boson Stars: Gravitational Equilibria of Selfinteracting Scalar Fields, Phys. Rev. Lett. 57 (1986) 2485 [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  81. [81]
    V. Cardoso, E. Franzin and P. Pani, Is the gravitational-wave ringdown a probe of the event horizon?, Phys. Rev. Lett. 116 (2016) 171101 [Erratum ibid. 117 (2016) 089902] [arXiv:1602.07309] [INSPIRE].
  82. [82]
    P.V.P. Cunha, E. Berti and C.A.R. Herdeiro, Light-Ring Stability for Ultracompact Objects, Phys. Rev. Lett. 119 (2017) 251102 [arXiv:1708.04211] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  83. [83]
    K. Dasgupta, M. Emelin, E. McDonough and R. Tatar, Quantum Corrections and the de Sitter Swampland Conjecture, JHEP 01 (2019) 145 [arXiv:1808.07498] [INSPIRE].CrossRefGoogle Scholar
  84. [84]
    U. Danielsson, The quantum swampland, arXiv:1809.04512 [INSPIRE].
  85. [85]
    T.W. Grimm, E. Palti and I. Valenzuela, Infinite Distances in Field Space and Massless Towers of States, JHEP 08 (2018) 143 [arXiv:1802.08264] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  86. [86]
    R. Blumenhagen, Large Field Inflation/Quintessence and the Refined Swampland Distance Conjecture, PoS(CORFU2017)175 (2018) [arXiv:1804.10504] [INSPIRE].
  87. [87]
    D. Andriot and C. Roupec, Further refining the de Sitter swampland conjecture, arXiv:1811.08889 [INSPIRE].
  88. [88]
    F. Denef, A. Hebecker and T. Wrase, de Sitter swampland conjecture and the Higgs potential, Phys. Rev. D 98 (2018) 086004 [arXiv:1807.06581] [INSPIRE].
  89. [89]
    J.P. Conlon, The de Sitter swampland conjecture and supersymmetric AdS vacua, Int. J. Mod. Phys. A 33 (2018) 1850178 [arXiv:1808.05040] [INSPIRE].ADSCrossRefGoogle Scholar
  90. [90]
    H. Murayama, M. Yamazaki and T.T. Yanagida, Do We Live in the Swampland?, JHEP 12 (2018) 032 [arXiv:1809.00478] [INSPIRE].ADSCrossRefGoogle Scholar
  91. [91]
    K. Choi, D. Chway and C.S. Shin, The dS swampland conjecture with the electroweak symmetry and QCD chiral symmetry breaking, JHEP 11 (2018) 142 [arXiv:1809.01475] [INSPIRE].ADSGoogle Scholar
  92. [92]
    K. Hamaguchi, M. Ibe and T. Moroi, The swampland conjecture and the Higgs expectation value, JHEP 12 (2018) 023 [arXiv:1810.02095] [INSPIRE].ADSCrossRefGoogle Scholar
  93. [93]
    M. Emelin and R. Tatar, Axion Hilltops, Kähler Modulus Quintessence and the Swampland Criteria, arXiv:1811.07378 [INSPIRE].
  94. [94]
    J. Blåbäck, U. Danielsson and G. Dibitetto, A new light on the darkest corner of the landscape, arXiv:1810.11365 [INSPIRE].
  95. [95]
    A. Arvanitaki, S. Dimopoulos, S. Dubovsky, N. Kaloper and J. March-Russell, String Axiverse, Phys. Rev. D 81 (2010) 123530 [arXiv:0905.4720] [INSPIRE].ADSGoogle Scholar
  96. [96]
    C.A.R. Herdeiro, E. Radu and H. Rúnarsson, Kerr black holes with self-interacting scalar hair: hairier but not heavier, Phys. Rev. D 92 (2015) 084059 [arXiv:1509.02923] [INSPIRE].ADSGoogle Scholar
  97. [97]
    G.H. Derrick, Comments on nonlinear wave equations as models for elementary particles, J. Math. Phys. 5 (1964) 1252 [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  98. [98]
    J. Balakrishna, E. Seidel and W.-M. Suen, Dynamical evolution of boson stars. 2. Excited states and selfinteracting fields, Phys. Rev. D 58 (1998) 104004 [gr-qc/9712064] [INSPIRE].
  99. [99]
    C.A.R. Herdeiro, E. Radu and H.F. Rúnarsson, Spinning boson stars and Kerr black holes with scalar hair: the effect of self-interactions, Int. J. Mod. Phys. D 25 (2016) 1641014 [arXiv:1604.06202] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  100. [100]
    P.V.P. Cunha, C.A.R. Herdeiro, E. Radu and H.F. Runarsson, Shadows of Kerr black holes with scalar hair, Phys. Rev. Lett. 115 (2015) 211102 [arXiv:1509.00021] [INSPIRE].ADSCrossRefzbMATHGoogle Scholar
  101. [101]
    C.A.R. Herdeiro and E. Radu, Asymptotically flat black holes with scalar hair: a review, Int. J. Mod. Phys. D 24 (2015) 1542014 [arXiv:1504.08209] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  102. [102]
    S. Hod, Stationary Scalar Clouds Around Rotating Black Holes, Phys. Rev. D 86 (2012) 104026 [Erratum ibid. D 86 (2012) 129902] [arXiv:1211.3202] [INSPIRE].
  103. [103]
    S. Hod, Stationary resonances of rapidly-rotating Kerr black holes, Eur. Phys. J. C 73 (2013) 2378 [arXiv:1311.5298] [INSPIRE].ADSCrossRefGoogle Scholar
  104. [104]
    S. Hod, Kerr-Newman black holes with stationary charged scalar clouds, Phys. Rev. D 90 (2014) 024051 [arXiv:1406.1179] [INSPIRE].ADSGoogle Scholar
  105. [105]
    C.L. Benone, L.C.B. Crispino, C. Herdeiro and E. Radu, Kerr-Newman scalar clouds, Phys. Rev. D 90 (2014) 104024 [arXiv:1409.1593] [INSPIRE].ADSGoogle Scholar
  106. [106]
    S. Hod, Spinning Kerr black holes with stationary massive scalar clouds: The large-coupling regime, JHEP 01 (2017) 030 [arXiv:1612.00014] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  107. [107]
    J.C. Degollado, C.A.R. Herdeiro and E. Radu, Effective stability against superradiance of Kerr black holes with synchronised hair, Phys. Lett. B 781 (2018) 651 [arXiv:1802.07266] [INSPIRE].ADSCrossRefGoogle Scholar

Copyright information

© The Author(s) 2019

Authors and Affiliations

  • Carlos A. R. Herdeiro
    • 1
  • Eugen Radu
    • 2
    • 3
  • Kunihito Uzawa
    • 4
    Email author
  1. 1.CENTRA, Departamento de Física, Instituto Superior TécnicoUniversidade de LisboaLisboaPortugal
  2. 2.School of Theoretical PhysicsDublin Institute for Advanced StudiesDublin 4Ireland
  3. 3.Center for Research and Development in Mathematics and ApplicationsAveiroPortugal
  4. 4.Department of Physics, School of Science and TechnologyKwansei Gakuin UniversitySandaJapan

Personalised recommendations