Skip to main content
SpringerLink
Log in

Self-completeness and the generalized uncertainty principle

  • Published:
Journal of High Energy Physics Aims and scope Submit manuscript

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

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

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

    Article  ADS  Google Scholar 

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

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  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].

    Article  ADS  Google Scholar 

  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].

    Article  ADS  Google Scholar 

  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].

    Article  MathSciNet  ADS  MATH  Google Scholar 

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

    Article  ADS  Google Scholar 

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

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

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

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

    Article  ADS  MATH  Google Scholar 

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

    Article  MathSciNet  ADS  Google Scholar 

  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].

    Article  MathSciNet  ADS  Google Scholar 

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

    Article  MathSciNet  ADS  Google Scholar 

  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].

    Article  MathSciNet  ADS  Google Scholar 

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

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

    Article  MathSciNet  ADS  MATH  Google Scholar 

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

  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].

    Article  MathSciNet  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  MathSciNet  ADS  Google Scholar 

  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].

    Article  MathSciNet  ADS  Google Scholar 

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

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

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

    Article  MATH  Google Scholar 

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

    Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  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. 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. 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].

    Article  MathSciNet  ADS  Google Scholar 

  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].

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  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].

    Article  MathSciNet  ADS  MATH  Google Scholar 

  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].

    Article  MathSciNet  ADS  Google Scholar 

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

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

    Article  ADS  Google Scholar 

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

    Article  MathSciNet  ADS  Google Scholar 

  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].

    Article  ADS  Google Scholar 

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

    Article  Google Scholar 

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

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

    ADS  Google Scholar 

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

    Article  MathSciNet  ADS  Google Scholar 

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

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

  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].

    Article  ADS  Google Scholar 

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

    Article  MathSciNet  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  Google Scholar 

  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. 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].

    Article  MathSciNet  ADS  Google Scholar 

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

    Article  MathSciNet  ADS  MATH  Google Scholar 

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

    Article  MathSciNet  ADS  MATH  Google Scholar 

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

    Article  MathSciNet  ADS  Google Scholar 

  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].

    Article  MathSciNet  ADS  Google Scholar 

  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].

    Article  MathSciNet  ADS  Google Scholar 

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

    Article  MathSciNet  ADS  Google Scholar 

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

    Article  MathSciNet  ADS  Google Scholar 

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

    Article  MathSciNet  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Physics, Loyola Marymount University, Los Angeles, CA, 90045-2659, U.S.A.

    Maximiliano Isi & Jonas Mureika

  2. Frankfurt Institute for Advanced Studies, Ruth-Moufang-Strasse 1, 60438, Frankfurt am Main, Germany

    Piero Nicolini

  3. Institut für Theoretische Physik, J.W. Goethe-Universität, Max-von-Laue-Strasse 1, 60438, Frankfurt am Main, Germany

    Piero Nicolini

Authors
  1. Maximiliano Isi
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Jonas Mureika
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Piero Nicolini
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Jonas Mureika.

Rights and permissions

Reprints and permissions

About this article

Cite this article

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

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/JHEP11(2013)139

Keywords

Search

Navigation