Horizon Quantum Mechanics: Spherically Symmetric and Rotating Sources

  • Roberto Casadio
  • Andrea Giugno
  • Andrea Giusti
  • Octavian Micu
Article
  • 20 Downloads

Abstract

The Horizon Quantum Mechanics is an approach that allows one to analyse the gravitational radius of spherically symmetric systems and compute the probability that a given quantum state is a black hole. We first review the (global) formalism and show how it reproduces a gravitationally inspired GUP relation. This results leads to unacceptably large fluctuations in the horizon size of astrophysical black holes if one insists in describing them as (smeared) central singularities. On the other hand, if they are extended systems, like in the corpuscular models, no such issue arises and one can in fact extend the formalism to include asymptotic mass and angular momentum with the harmonic model of rotating corpuscular black holes. The Horizon Quantum Mechanics then shows that, in simple configurations, the appearance of the inner horizon is suppressed and extremal (macroscopic) geometries seem disfavoured.

Keywords

Quantum black holes Corpuscular model Rotating black holes 

Notes

Acknowledgements

R.C. and A.G. are partially supported by the INFN grant FLAG. The work of R.C. and A.G. has also been carried out in the framework of activities of the National Group of Mathematical Physics (GNFM, INdAM). O.M. was supported by the grant LAPLAS 4.

References

  1. 1.
    Casadio, R.: Localised particles and fuzzy horizons: A tool for probing Quantum Black Holes. arXiv:1305.3195 [gr-qc]
  2. 2.
    Casadio, R.: What is the Schwarzschild radius of a quantum mechanical particle? Springer Proceedings in Physics 170, 225 (2016). arXiv:1310.5452 [gr-qc]
  3. 3.
    Casadio, R., Giugno, A., Giusti, A.: Global and local horizon quantum mechanics. Gen. Rel. Grav. 49, 32 (2017). [arXiv:1605.06617 [gr-qc]]ADSMathSciNetCrossRefMATHGoogle Scholar
  4. 4.
    Casadio, R., Scardigli, F.: Horizon wave-function for single localized particles: GUP and quantum black hole decay. Eur. Phys. J. C 74, 2685 (2014). [arXiv:1306.5298 [gr-qc]]ADSCrossRefGoogle Scholar
  5. 5.
    Casadio, R., Micu, O., Scardigli, F.: Quantum hoop conjecture: black hole formation by particle collisions. Phys. Lett. B 732, 105 (2014). [arXiv:1311.5698 [hep-th]]ADSMathSciNetCrossRefMATHGoogle Scholar
  6. 6.
    Casadio, R., Micu, O., Stojkovic, D.: Inner horizon of the quantum Reissner–Nordström black holes. JHEP 1505, 096 (2015). arXiv:1503.01888 [gr-qc]
  7. 7.
    Casadio, R., Micu, O., Stojkovic, D.: Horizon wave-function and the quantum cosmic censorship. Phys. Lett. B 747, 68 (2015). arXiv:1503.02858 [gr-qc]
  8. 8.
    Casadio, R., Giugno, A., Micu, O.: Horizon quantum mechanics: a hitchhiker’s guide to quantum black holes. Int. J. Mod. Phys. D 25, 1630006 (2016). arXiv:1512.04071 [hep-th]
  9. 9.
    Casadio, R., Giugno, A., Giusti, A., Micu, O.: Horizon quantum mechanics of rotating black holes. Eur. Phys. J. C 77(5), 322 (2017). arXiv:1701.05778 [gr-qc]
  10. 10.
    Szabados, L.B.: Quasi-local energy-momentum and angular momentum in general relativity. Living Rev. Relat. 12, 4 (2009)ADSCrossRefMATHGoogle Scholar
  11. 11.
    Casadio, R., Orlandi, A.: Quantum harmonic black holes. JHEP 1308, 025 (2013). arXiv:1302.7138 [hep-th]
  12. 12.
    Mück, W., Pozzo, G.: Quantum portrait of a black hole with Pöschl-Teller potential. JHEP 1405, 128 (2014). arXiv:1403.1422 [hep-th]
  13. 13.
    Dvali, G., Gomez, C.: Quantum compositeness of gravity: black holes, AdS and inflation. JCAP 01, 023 (2014). arXiv:1312.4795 [hep-th]
  14. 14.
    Dvali, G., Gomez, C.: Black Hole’s Information Group. arXiv:1307.7630
  15. 15.
    Dvali, G., Gomez, C.: Black holes as critical point of quantum phase transition. Eur. Phys. J. C 74, 2752 (2014). arXiv:1207.4059 [hep-th]
  16. 16.
    Dvali, G., Gomez, C.: Black hole’s 1/N hair. Phys. Lett. B 719, 419 (2013). arXiv:1203.6575 [hep-th]
  17. 17.
    Dvali, G., Gomez, C.: Landau–Ginzburg limit of black hole’s quantum portrait: self similarity and critical exponent. Phys. Lett. B 716, 240 (2012). arXiv:1203.3372 [hep-th]
  18. 18.
    Dvali, G., Gomez, C.: Black hole’s quantum N-portrait. Fortsch. Phys. 61, 742 (2013). arXiv:1112.3359 [hep-th]
  19. 19.
    Dvali, G., Gomez, C., Mukhanov, S.: Black hole masses are quantized. arXiv:1106.5894 [hep-ph]
  20. 20.
    Casadio, R., Giugno, A., Micu, O., Orlandi, A.: Thermal BEC black holes. Entropy 17, 6893 (2015). arXiv:1511.01279 [gr-qc]
  21. 21.
    Arnowitt, R.L., Deser, S., Misner, C.W.: Dynamical structure and definition of energy in general relativity. Phys. Rev. 116, 1322 (1959)ADSMathSciNetCrossRefMATHGoogle Scholar
  22. 22.
    Thorne, K.S.: Nonspherical gravitational collapse: a short review. In: Klauder, J.R. (ed.) Magic Without Magic, p. 231. Freeman, San Francisco (1972)Google Scholar
  23. 23.
    Casadio, R., Giugno, A., Giusti, A.: Matter and gravitons in the gravitational collapse. Phys. Lett. B 763, 337 (2016). arXiv:1606.04744 [hep-th]

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Dipartimento di Fisica e AstronomiaUniversità di BolognaBolognaItaly
  2. 2.I.N.F.N., Sezione di BolognaBolognaItaly
  3. 3.Arnold Sommerfeld Center, Ludwig-Maximilians-UniversitätMünchenGermany
  4. 4.Institute of Space ScienceBucharest-MagureleRomania

Personalised recommendations