Self-completeness and the generalized uncertainty principle

Abstract

The generalized uncertainty principle discloses a self-complete characteristic of gravity, namely the possibility of masking any curvature singularity behind an event horizon as a result of matter compression at the Planck scale. In this paper we extend the above reasoning in order to overcome some current limitations to the framework, including the absence of a consistent metric describing such Planck-scale black holes. We implement a minimum-size black hole in terms of the extremal configuration of a neutral non-rotating metric, which we derived by mimicking the effects of the generalized uncertainty principle via a short scale modified version of Einstein gravity. In such a way, we find a self-consistent scenario that reconciles the self-complete character of gravity and the generalized uncertainty principle.

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References

  1. [1]

    A. Kempf, G. Mangano and R.B. Mann, Hilbert space representation of the minimal length uncertainty relation, Phys. Rev. D 52 (1995) 1108 [hep-th/9412167] [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  2. [2]

    G. Dvali and C. Gomez, Self-Completeness of Einstein Gravity, arXiv:1005.3497 [INSPIRE].

  3. [3]

    G. Dvali, S. Folkerts and C. Germani, Physics of Trans-Planckian Gravity, Phys. Rev. D 84 (2011) 024039 [arXiv:1006.0984] [INSPIRE].

    ADS  Google Scholar 

  4. [4]

    G. Dvali and C. Gomez, Ultra-high energy probes of classicalization, JCAP 07 (2012) 015 [arXiv:1205.2540] [INSPIRE].

    ADS  Article  Google Scholar 

  5. [5]

    A. Aurilia and E. spallucci, Plancks uncertainty principle and the saturation of Lorentz boosts by Planckian black holes, arXiv:1309.7186 [INSPIRE].

  6. [6]

    M. Maggiore, A generalized uncertainty principle in quantum gravity, Phys. Lett. B 304 (1993) 65 [hep-th/9301067] [INSPIRE].

    ADS  Article  Google Scholar 

  7. [7]

    L.J. Garay, Quantum gravity and minimum length, Int. J. Mod. Phys. A 10 (1995) 145 [gr-qc/9403008] [INSPIRE].

    ADS  Article  Google Scholar 

  8. [8]

    F. Scardigli, Generalized uncertainty principle in quantum gravity from micro-black hole Gedanken experiment, Phys. Lett. B 452 (1999) 39 [hep-th/9904025] [INSPIRE].

    ADS  Article  Google Scholar 

  9. [9]

    R.J. Adler and D.I. Santiago, On gravity and the uncertainty principle, Mod. Phys. Lett. A 14 (1999) 1371 [gr-qc/9904026] [INSPIRE].

    ADS  Article  Google Scholar 

  10. [10]

    R.J. Adler, P. Chen and D.I. Santiago, The generalized uncertainty principle and black hole remnants, Gen. Rel. Grav. 33 (2001) 2101 [gr-qc/0106080] [INSPIRE].

    MathSciNet  ADS  Article  MATH  Google Scholar 

  11. [11]

    R.J. Adler, Six easy roads to the Planck scale, Am. J. Phys. 78 (2010) 925 [arXiv:1001.1205] [INSPIRE].

    ADS  Article  Google Scholar 

  12. [12]

    R. Casadio and F. Scardigli, Horizon wave-function for single localized particles: GUP and quantum black hole decay, arXiv:1306.5298 [INSPIRE].

  13. [13]

    G. Veneziano, A stringy nature needs just two constants, Europhys. Lett. 2 (1986) 199 [INSPIRE].

    ADS  Article  Google Scholar 

  14. [14]

    D. Amati, M. Ciafaloni and G. Veneziano, Can Space-Time Be Probed Below the String Size?, Phys. Lett. B 216 (1989) 41 [INSPIRE].

    ADS  Article  Google Scholar 

  15. [15]

    A. Aurilia and E. Spallucci, Why the length of a quantum string cannot be Lorentz contracted, arXiv:1309.7741 [INSPIRE].

  16. [16]

    P. Chen and R.J. Adler, Black hole remnants and dark matter, Nucl. Phys. Proc. Suppl. 124 (2003) 103 [gr-qc/0205106] [INSPIRE].

    ADS  Article  MATH  Google Scholar 

  17. [17]

    P. Nicolini, A. Smailagic and E. Spallucci, Noncommutative geometry inspired Schwarzschild black hole, Phys. Lett. B 632 (2006) 547 [gr-qc/0510112] [INSPIRE].

    MathSciNet  ADS  Article  Google Scholar 

  18. [18]

    P. Nicolini, Noncommutative black holes, the final appeal to quantum gravity: a review, Int. J. Mod. Phys. A 24 (2009) 1229 [arXiv:0807.1939] [INSPIRE].

    MathSciNet  ADS  Article  Google Scholar 

  19. [19]

    P. Nicolini and E. Spallucci, Noncommutative geometry inspired wormholes and dirty black holes, Class. Quant. Grav. 27 (2010) 015010 [arXiv:0902.4654] [INSPIRE].

    MathSciNet  ADS  Article  Google Scholar 

  20. [20]

    L. Modesto, J.W. Moffat and P. Nicolini, Black holes in an ultraviolet complete quantum gravity, Phys. Lett. B 695 (2011) 397 [arXiv:1010.0680] [INSPIRE].

    MathSciNet  ADS  Article  Google Scholar 

  21. [21]

    P. Nicolini, Nonlocal and generalized uncertainty principle black holes, arXiv:1202.2102 [INSPIRE].

  22. [22]

    A. Bonanno and M. Reuter, Renormalization group improved black hole space-times, Phys. Rev. D 62 (2000) 043008 [hep-th/0002196] [INSPIRE].

    ADS  Google Scholar 

  23. [23]

    L. Modesto, Loop quantum black hole, Class. Quant. Grav. 23 (2006) 5587 [gr-qc/0509078] [INSPIRE].

    MathSciNet  ADS  Article  MATH  Google Scholar 

  24. [24]

    L. Modesto and I. Premont-Schwarz, Self-dual Black Holes in LQG: Theory and Phenomenology, Phys. Rev. D 80 (2009) 064041 [arXiv:0905.3170] [INSPIRE].

    ADS  Google Scholar 

  25. [25]

    S. Hossenfelder, L. Modesto and I. Premont-Schwarz, A model for non-singular black hole collapse and evaporation, Phys. Rev. D 81 (2010) 044036 [arXiv:0912.1823] [INSPIRE].

    ADS  Google Scholar 

  26. [26]

    B. Carr, L. Modesto and I. Premont-Schwarz, Generalized Uncertainty Principle and Self-dual Black Holes, arXiv:1107.0708 [INSPIRE].

  27. [27]

    J. Mureika and E. Spallucci, Vector unparticle enhanced black holes: exact solutions and thermodynamics, Phys. Lett. B 693 (2010) 129 [arXiv:1006.4556] [INSPIRE].

    MathSciNet  ADS  Article  Google Scholar 

  28. [28]

    S.A. Hayward, Formation and evaporation of regular black holes, Phys. Rev. Lett. 96 (2006) 031103 [gr-qc/0506126] [INSPIRE].

    ADS  Article  Google Scholar 

  29. [29]

    E. Spallucci and A. Smailagic, Black holes production in self-complete quantum gravity, Phys. Lett. B 709 (2012) 266 [arXiv:1202.1686] [INSPIRE].

    MathSciNet  ADS  Article  Google Scholar 

  30. [30]

    E. Spallucci and S. Ansoldi, Regular black holes in UV self-complete quantum gravity, Phys. Lett. B 701 (2011) 471 [arXiv:1101.2760] [INSPIRE].

    MathSciNet  ADS  Article  Google Scholar 

  31. [31]

    P. Nicolini and E. Spallucci, Holographic screens in ultraviolet self-complete quantum gravity, arXiv:1210.0015 [INSPIRE].

  32. [32]

    J. Mureika and P. Nicolini, Self-completeness and spontaneous dimensional reduction, Eur. Phys. J. Plus (2013) 128: 78 [arXiv:1206.4696] [INSPIRE].

  33. [33]

    M. Sprenger, P. Nicolini and M. Bleicher, Physics on smallest scalesan introduction to minimal length phenomenology, Eur. J. Phys. 33 (2012) 853 [arXiv:1202.1500] [INSPIRE].

    Article  MATH  Google Scholar 

  34. [34]

    S. Hossenfelder, Minimal length scale scenarios for quantum gravity, Living Rev. Rel. 16 (2013) 2 [arXiv:1203.6191] [INSPIRE].

    Google Scholar 

  35. [35]

    L.B. Crowell, Generalized uncertainty principle for quantum fields in curved space-time, Found. Phys. Lett. 12 (1999) 585 [INSPIRE].

    MathSciNet  Article  Google Scholar 

  36. [36]

    V. Husain, D. Kothawala and S.S. Seahra, Generalized uncertainty principles and quantum field theory, Phys. Rev. D 87 (2013) 025014 [arXiv:1208.5761] [INSPIRE].

    ADS  Google Scholar 

  37. [37]

    M. Kober, Gauge Theories under Incorporation of a Generalized Uncertainty Principle, Phys. Rev. D 82 (2010) 085017 [arXiv:1008.0154] [INSPIRE].

    ADS  Google Scholar 

  38. [38]

    T. Zhu, J.-R. Ren and M.-F. Li, Influence of Generalized and Extended Uncertainty Principle on Thermodynamics of FRW universe, Phys. Lett. B 674 (2009) 204 [arXiv:0811.0212] [INSPIRE].

    MathSciNet  ADS  Article  Google Scholar 

  39. [39]

    W. Kim, Y.-J. Park and M. Yoon, Entropy of the FRW universe based on the generalized uncertainty principle, Mod. Phys. Lett. A 25 (2010) 1267 [arXiv:1003.3287] [INSPIRE].

    ADS  Article  Google Scholar 

  40. [40]

    S. Hossenfelder et al., Collider signatures in the Planck regime, Phys. Lett. B 575 (2003) 85 [hep-th/0305262] [INSPIRE].

    ADS  Article  Google Scholar 

  41. [41]

    G. Amelino-Camelia, M. Arzano, Y. Ling and G. Mandanici, Black-hole thermodynamics with modified dispersion relations and generalized uncertainty principles, Class. Quant. Grav. 23 (2006) 2585 [gr-qc/0506110] [INSPIRE].

    MathSciNet  ADS  Article  MATH  Google Scholar 

  42. [42]

    Y.S. Myung, Y.-W. Kim and Y.-J. Park, Black hole thermodynamics with generalized uncertainty principle, Phys. Lett. B 645 (2007) 393 [gr-qc/0609031] [INSPIRE].

    MathSciNet  ADS  Article  Google Scholar 

  43. [43]

    A. Bina, S. Jalalzadeh and A. Moslehi, Quantum Black Hole in the Generalized Uncertainty Principle Framework, Phys. Rev. D 81 (2010) 023528 [arXiv:1001.0861] [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  44. [44]

    S. Gangopadhyay, A. Dutta and A. Saha, Generalized uncertainty principle and black hole thermodynamics, arXiv:1307.7045 [INSPIRE].

  45. [45]

    B. Koch, M. Bleicher and S. Hossenfelder, Black hole remnants at the LHC, JHEP 10 (2005) 053 [hep-ph/0507138] [INSPIRE].

    ADS  Article  Google Scholar 

  46. [46]

    M. Maziashvili, Black hole remnants due to GUP or quantum gravity?, Phys. Lett. B 635 (2006) 232 [gr-qc/0511054] [INSPIRE].

    MathSciNet  ADS  Article  Google Scholar 

  47. [47]

    D. Mania and M. Maziashvili, Corrections to the black body radiation due to minimum-length deformed quantum mechanics, Phys. Lett. B 705 (2011) 521 [arXiv:0911.1197] [INSPIRE].

    ADS  Article  Google Scholar 

  48. [48]

    A.R.P. Dirkes, M. Maziashvili and Z.K. Silagadze, Black hole remnants due to Planck-length deformed QFT, arXiv:1309.7427 [INSPIRE].

  49. [49]

    N. Krasnikov, Nonlocal gauge theories, Theor. Math. Phys. 73 (1987) 1184 [INSPIRE].

    Article  Google Scholar 

  50. [50]

    E. Tomboulis, Superrenormalizable gauge and gravitational theories, hep-th/9702146 [INSPIRE].

  51. [51]

    L. Modesto, Super-renormalizable Quantum Gravity, Phys. Rev. D 86 (2012) 044005 [arXiv:1107.2403] [INSPIRE].

    ADS  Google Scholar 

  52. [52]

    L. Modesto and S. Tsujikawa, Non-local massive gravity, Phys. Lett. B 727 (2013) 48 [arXiv:1307.6968] [INSPIRE].

    MathSciNet  ADS  Article  Google Scholar 

  53. [53]

    F. Briscese, L. Modesto and S. Tsujikawa, Super-renormalizable or finite completion of the Starobinsky theory, arXiv:1308.1413 [INSPIRE].

  54. [54]

    G. Calcagni, L. Modesto and P. Nicolini, Super-accelerating bouncing cosmology in asymptotically-free non-local gravity, arXiv:1306.5332 [INSPIRE].

  55. [55]

    T. Biswas, E. Gerwick, T. Koivisto and A. Mazumdar, Towards singularity and ghost free theories of gravity, Phys. Rev. Lett. 108 (2012) 031101 [arXiv:1110.5249] [INSPIRE].

    ADS  Article  Google Scholar 

  56. [56]

    A. Barvinsky, Nonlocal action for long distance modifications of gravity theory, Phys. Lett. B 572 (2003) 109 [hep-th/0304229] [INSPIRE].

    MathSciNet  ADS  Article  Google Scholar 

  57. [57]

    A. Barvinsky, On covariant long-distance modifications of Einstein theory and strong coupling problem, Phys. Rev. D 71 (2005) 084007 [hep-th/0501093] [INSPIRE].

    ADS  Google Scholar 

  58. [58]

    A. Barvinsky, Dark energy and dark matter from nonlocal ghost-free gravity theory, Phys. Lett. B 710 (2012) 12 [arXiv:1107.1463] [INSPIRE].

    ADS  Article  Google Scholar 

  59. [59]

    J. Moffat, Ultraviolet complete quantum gravity, Eur. Phys. J. Plus 126 (2011) 43 [arXiv:1008.2482] [INSPIRE].

    Article  Google Scholar 

  60. [60]

    S. Weinberg, Ultraviolet Divergences In Quantum Theories Of Gravitation, in General Relativity: An Einstein centenary survey, S.W. Hawking and W. Israel eds., Cambridge University Press, Cambridge U.K. (1980), pg. 790.

    Google Scholar 

  61. [61]

    P. Gaete, J.A. Helayel-Neto and E. Spallucci, Un-graviton corrections to the Schwarzschild black hole, Phys. Lett. B 693 (2010) 155 [arXiv:1005.0234] [INSPIRE].

    MathSciNet  ADS  Article  Google Scholar 

  62. [62]

    G.V. Efimov, Non-local quantum theory of the scalar field, Commun. Math. Phys. 5 (1967) 42.

    MathSciNet  ADS  Article  MATH  Google Scholar 

  63. [63]

    G.V. Efimov, On a class of relativistic invariant distributions, Commun. Math. Phys. 7 (1968) 138.

    MathSciNet  ADS  Article  MATH  Google Scholar 

  64. [64]

    T.G. Rizzo, Noncommutative inspired black holes in extra dimensions, JHEP 09 (2006) 021 [hep-ph/0606051] [INSPIRE].

    MathSciNet  ADS  Article  Google Scholar 

  65. [65]

    S. Ansoldi, P. Nicolini, A. Smailagic and E. Spallucci, Noncommutative geometry inspired charged black holes, Phys. Lett. B 645 (2007) 261 [gr-qc/0612035] [INSPIRE].

    MathSciNet  ADS  Article  Google Scholar 

  66. [66]

    E. Spallucci, A. Smailagic and P. Nicolini, Non-commutative geometry inspired higher-dimensional charged black holes, Phys. Lett. B 670 (2009) 449 [arXiv:0801.3519] [INSPIRE].

    MathSciNet  ADS  Article  Google Scholar 

  67. [67]

    A. Smailagic and E. Spallucci, ’Kerrrblack hole: the Lord of the String, Phys. Lett. B 688 (2010) 82 [arXiv:1003.3918] [INSPIRE].

    MathSciNet  ADS  Article  Google Scholar 

  68. [68]

    L. Modesto and P. Nicolini, Charged rotating noncommutative black holes, Phys. Rev. D 82 (2010) 104035 [arXiv:1005.5605] [INSPIRE].

    ADS  Google Scholar 

  69. [69]

    J.R. Mureika and P. Nicolini, Aspects of noncommutative (1 + 1)-dimensional black holes, Phys. Rev. D 84 (2011) 044020 [arXiv:1104.4120] [INSPIRE].

    ADS  Google Scholar 

  70. [70]

    A. Smailagic and E. Spallucci, Lorentz invariance, unitarity in UV-finite of QFT on noncommutative spacetime, J. Phys. A 37 (2004) 1 [Erratum ibid. A 37 (2004) 7169] [hep-th/0406174] [INSPIRE].

  71. [71]

    E. Spallucci, A. Smailagic and P. Nicolini, Trace Anomaly in Quantum Spacetime Manifold, Phys. Rev. D 73 (2006) 084004 [hep-th/0604094] [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  72. [72]

    M. Kober and P. Nicolini, Minimal Scales from an Extended Hilbert Space, Class. Quant. Grav. 27 (2010) 245024 [arXiv:1005.3293] [INSPIRE].

    MathSciNet  ADS  Article  Google Scholar 

  73. [73]

    P. Nicolini and E. Winstanley, Hawking emission from quantum gravity black holes, JHEP 11 (2011) 075 [arXiv:1108.4419] [INSPIRE].

    MathSciNet  ADS  Article  Google Scholar 

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Correspondence to Jonas Mureika.

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Isi, M., Mureika, J. & Nicolini, P. Self-completeness and the generalized uncertainty principle. J. High Energ. Phys. 2013, 139 (2013). https://doi.org/10.1007/JHEP11(2013)139

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Keywords

  • Models of Quantum Gravity
  • Black Holes