One thousand and one bubbles

  • Jesús Ávila
  • Pedro F. Ramírez
  • Alejandro Ruipérez
Open Access
Regular Article - Theoretical Physics

Abstract

We propose a novel strategy that permits the construction of completely general five-dimensional microstate geometries on a Gibbons-Hawking space. Our scheme is based on two steps. First, we rewrite the bubble equations as a system of linear equations that can be easily solved. Second, we conjecture that the presence or absence of closed timelike curves in the solution can be detected through the evaluation of an algebraic relation. The construction we propose is systematic and covers the whole space of parameters, so it can be applied to find all five-dimensional BPS microstate geometries on a Gibbons-Hawking base. As a first result of this approach, we find that the spectrum of scaling solutions becomes much larger when non-Abelian fields are present. We use our method to describe several smooth horizonless multicenter solutions with the asymptotic charges of three-charge (Abelian and non-Abelian) black holes. In particular, we describe solutions with the centers lying on lines and circles that can be specified with exact precision. We show the power of our method by explicitly constructing a 50-center solution. Moreover, we use it to find the first smooth five-dimensional microstate geometries with arbitrarily small angular momentum.

Keywords

Black Holes in String Theory Gauge Symmetry 

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]
    A. Einstein and W. Pauli, On the non-existence of regular stationary solutions of relativistic field equations, Annals Math. 44 (1943) 131.MathSciNetCrossRefMATHGoogle Scholar
  2. [2]
    G.W. Gibbons and N.P. Warner, Global structure of five-dimensional fuzzballs, Class. Quant. Grav. 31 (2014) 025016 [arXiv:1305.0957] [INSPIRE].ADSCrossRefMATHGoogle Scholar
  3. [3]
    R. Bartnik and J. Mckinnon, Particle-Like Solutions of the Einstein Yang-Mills Equations, Phys. Rev. Lett. 61 (1988) 141 [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  4. [4]
    A. Strominger, Heterotic solitons, Nucl. Phys. B 343 (1990) 167 [Erratum ibid. B 353 (1991) 565] [INSPIRE].
  5. [5]
    J.A. Harvey and J. Liu, Magnetic monopoles in N = 4 supersymmetric low-energy superstring theory, Phys. Lett. B 268 (1991) 40 [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  6. [6]
    A.H. Chamseddine and M.S. Volkov, NonAbelian BPS monopoles in N = 4 gauged supergravity, Phys. Rev. Lett. 79 (1997) 3343 [hep-th/9707176] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  7. [7]
    A.H. Chamseddine and M.S. Volkov, NonAbelian solitons in N = 4 gauged supergravity and leading order string theory, Phys. Rev. D 57 (1998) 6242 [hep-th/9711181] [INSPIRE].ADSGoogle Scholar
  8. [8]
    M. Huebscher, P. Meessen, T. Ortín and S. Vaula, N = 2 Einstein-Yang-Mills’s BPS solutions, JHEP 09 (2008) 099 [arXiv:0806.1477] [INSPIRE].
  9. [9]
    P. Bueno, P. Meessen, T. Ortín and P.F. Ramírez, \( \mathcal{N}=2 \) Einstein-Yang-Mills’ static two-center solutions, JHEP 12 (2014) 093 [arXiv:1410.4160] [INSPIRE].
  10. [10]
    P.A. Cano, T. Ortín and P.F. Ramírez, A gravitating Yang-Mills instanton, JHEP 07 (2017) 011 [arXiv:1704.00504] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  11. [11]
    P.F. Ramírez, Non-Abelian bubbles in microstate geometries, JHEP 11 (2016) 152 [arXiv:1608.01330] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  12. [12]
    P. Berglund, E.G. Gimon and T.S. Levi, Supergravity microstates for BPS black holes and black rings, JHEP 06 (2006) 007 [hep-th/0505167] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  13. [13]
    I. Bena and N.P. Warner, Bubbling supertubes and foaming black holes, Phys. Rev. D 74 (2006) 066001 [hep-th/0505166] [INSPIRE].ADSMathSciNetGoogle Scholar
  14. [14]
    S.D. Mathur, The fuzzball proposal for black holes: An elementary review, Fortsch. Phys. 53 (2005) 793 [hep-th/0502050] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  15. [15]
    O. Lunin and S.D. Mathur, AdS/CFT duality and the black hole information paradox, Nucl. Phys. B 623 (2002) 342 [hep-th/0109154] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  16. [16]
    O. Lunin, J.M. Maldacena and L. Maoz, Gravity solutions for the D1-D5 system with angular momentum, hep-th/0212210 [INSPIRE].
  17. [17]
    S.D. Mathur, A. Saxena and Y.K. Srivastava, Constructing ‘hair’ for the three charge hole, Nucl. Phys. B 680 (2004) 415 [hep-th/0311092] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  18. [18]
    O. Lunin, Adding momentum to D1-D5 system, JHEP 04 (2004) 054 [hep-th/0404006] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  19. [19]
    S. Giusto, S.D. Mathur and A. Saxena, Dual geometries for a set of 3-charge microstates, Nucl. Phys. B 701 (2004) 357 [hep-th/0405017] [INSPIRE].
  20. [20]
    S. Giusto, S.D. Mathur and A. Saxena, 3-charge geometries and their CFT duals, Nucl. Phys. B 710 (2005) 425 [hep-th/0406103] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  21. [21]
    S. Giusto and S.D. Mathur, Geometry of D1-D5-P bound states, Nucl. Phys. B 729 (2005) 203 [hep-th/0409067] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  22. [22]
    J.B. Gutowski and H.S. Reall, General supersymmetric AdS5 black holes, JHEP 04 (2004) 048 [hep-th/0401129] [INSPIRE].
  23. [23]
    I. Bena and N.P. Warner, One ring to rule them all. . . and in the darkness bind them?, Adv. Theor. Math. Phys. 9 (2005) 667 [hep-th/0408106] [INSPIRE].MathSciNetCrossRefMATHGoogle Scholar
  24. [24]
    J. Bellorín and T. Ortín, Characterization of all the supersymmetric solutions of gauged N = 1, D = 5 supergravity, JHEP 08 (2007) 096 [arXiv:0705.2567] [INSPIRE].
  25. [25]
    P. Meessen, Supersymmetric coloured/hairy black holes, Phys. Lett. B 665 (2008) 388 [arXiv:0803.0684] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  26. [26]
    P. Bueno, P. Meessen, T. Ortín and P.F. Ramírez, Resolution of SU(2) monopole singularities by oxidation, Phys. Lett. B 746 (2015) 109 [arXiv:1503.01044] [INSPIRE].
  27. [27]
    P. Meessen, T. Ortín and P.F. Ramírez, Non-Abelian, supersymmetric black holes and strings in 5 dimensions, JHEP 03 (2016) 112 [arXiv:1512.07131] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  28. [28]
    T. Ortín and P.F. Ramírez, A non-Abelian Black Ring, Phys. Lett. B 760 (2016) 475 [arXiv:1605.00005] [INSPIRE].
  29. [29]
    P.A. Cano, T. Ortíın and C. Santoli, Non-Abelian black string solutions of \( \mathcal{N}=\left(2,0\right) \), d = 6 supergravity, JHEP 12 (2016) 112 [arXiv:1607.02595] [INSPIRE].
  30. [30]
    P.A. Cano, P. Meessen, T. Ortín and P.F. Ramírez, Non-Abelian black holes in string theory, JHEP 12 (2017) 092 [arXiv:1704.01134] [INSPIRE].ADSCrossRefGoogle Scholar
  31. [31]
    P. Meessen, T. Ortín and P.F. Ramírez, Dyonic black holes at arbitrary locations, JHEP 10 (2017) 066 [arXiv:1707.03846] [INSPIRE].ADSCrossRefGoogle Scholar
  32. [32]
    J.J. Fernández-Melgarejo, M. Park and M. Shigemori, Non-Abelian Supertubes, JHEP 12 (2017) 103 [arXiv:1709.02388] [INSPIRE].ADSCrossRefGoogle Scholar
  33. [33]
    E.G. Gimon and T.S. Levi, Black Ring Deconstruction, JHEP 04 (2008) 098 [arXiv:0706.3394] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  34. [34]
    I. Bena and N.P. Warner, Black holes, black rings and their microstates, Lect. Notes Phys. 755 (2008) 1 [hep-th/0701216] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  35. [35]
    I. Bena, C.-W. Wang and N.P. Warner, Mergers and typical black hole microstates, JHEP 11 (2006) 042 [hep-th/0608217] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  36. [36]
    I. Bena, C.-W. Wang and N.P. Warner, Plumbing the Abyss: Black ring microstates, JHEP 07 (2008) 019 [arXiv:0706.3786] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  37. [37]
    I. Bena, N. Bobev and N.P. Warner, Spectral Flow and the Spectrum of Multi-Center Solutions, Phys. Rev. D 77 (2008) 125025 [arXiv:0803.1203] [INSPIRE].ADSGoogle Scholar
  38. [38]
    P. Heidmann, Four-center bubbled BPS solutions with a Gibbons-Hawking base, JHEP 10 (2017) 009 [arXiv:1703.10095] [INSPIRE].ADSCrossRefGoogle Scholar
  39. [39]
    I. Bena, P. Heidmann and P.F. Ramírez, A systematic construction of microstate geometries with low angular momentum, JHEP 10 (2017) 217 [arXiv:1709.02812] [INSPIRE].
  40. [40]
    I. Bena, M. Shigemori and N.P. Warner, Black-Hole Entropy from Supergravity Superstrata States, JHEP 10 (2014) 140 [arXiv:1406.4506] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  41. [41]
    I. Bena et al., Smooth horizonless geometries deep inside the black-hole regime, Phys. Rev. Lett. 117 (2016) 201601 [arXiv:1607.03908] [INSPIRE].ADSCrossRefGoogle Scholar
  42. [42]
    G.W. Gibbons and S.W. Hawking, Gravitational Multi-Instantons, Phys. Lett. B 78 (1978) 430 [INSPIRE].ADSCrossRefGoogle Scholar
  43. [43]
    G.W. Gibbons and P.J. Ruback, The Hidden Symmetries of Multicenter Metrics, Commun. Math. Phys. 115 (1988) 267 [INSPIRE].ADSCrossRefMATHGoogle Scholar
  44. [44]
    C.W. Misner, The flatter regions of Newman, Unti and Tamburino’s generalized Schwarzschild space, J. Math. Phys. 4 (1963) 924 [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  45. [45]
    L. Infeld and P.R. Wallace, The Equations of Motion in Electrodynamics, Phys. Rev. 57 (1940) 797 [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  46. [46]
    T. Ortín, Gravity and Strings, Cambridge Monographs on Mathematical Physics, Cambridge University Press, (2015).Google Scholar
  47. [47]
    B.E. Niehoff and H.S. Reall, Evanescent ergosurfaces and ambipolar hyperkähler metrics, JHEP 04 (2016) 130 [arXiv:1601.01898] [INSPIRE].ADSGoogle Scholar
  48. [48]
    J. Ávila, P. Heidmann, P.F. Ramírez and A. Ruipérez, work in progress.Google Scholar
  49. [49]
    N.H. Anning and P. Erdös, Integral distances, Bull. Amer. Math. Soc. 51 (1945) 598.Google Scholar
  50. [50]
    I. Bena, D. Turton, R. Walker and N.P. Warner, Integrability and Black-Hole Microstate Geometries, JHEP 11 (2017) 021 [arXiv:1709.01107] [INSPIRE].ADSCrossRefGoogle Scholar
  51. [51]
    F.C. Eperon, Geodesics in supersymmetric microstate geometries, Class. Quant. Grav. 34 (2017) 165003 [arXiv:1702.03975] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  52. [52]
    F.C. Eperon, H.S. Reall and J.E. Santos, Instability of supersymmetric microstate geometries, JHEP 10 (2016) 031 [arXiv:1607.06828] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  53. [53]
    J. Keir, Wave propagation on microstate geometries, arXiv:1609.01733 [INSPIRE].
  54. [54]
    D. Marolf, B. Michel and A. Puhm, A rough end for smooth microstate geometries, JHEP 05 (2017) 021 [arXiv:1612.05235] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar

Copyright information

© The Author(s) 2018

Authors and Affiliations

  • Jesús Ávila
    • 1
  • Pedro F. Ramírez
    • 2
  • Alejandro Ruipérez
    • 2
  1. 1.Instituto de Ciencia de Materiales de Madrid ICMM/CSICMadridSpain
  2. 2.Instituto de Física Teórica UAM/CSICMadridSpain

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