Abstract
For a quantum mechanically Gaussian shaped, electrically charged, massive particle, we compute the Horizon Wave-function(s) in order to study (a) the existence of the inner Cauchy horizon of the corresponding Reissner–Nordström space-time when the charge-to-mass ratio \(0<\alpha <1\) and (b) the survival of a naked singularity when the charge-to-mass ratio \(\alpha >1\). Our results suggest that any semiclassical instability one expects near the inner horizon may not occur in quantum black holes, with a mass around the Planck scale, and that no states with charge-to-mass ratio greater than a critical value (of the order of \(\sqrt{2}\)) should exist.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
R. Casadio, Localised particles and fuzzy horizons: a tool for probing quantum black holes, arXiv:1305.3195 [gr-qc]; R. Casadio, F. Scardigli, 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]; X. Calmet, R. Casadio, The horizon of the lightest black hole, arXiv:1509.02055 [hep-th]
R. Casadio, Horizons and non-local time evolution of quantum mechanical systems. Eur. Phys. J. C 75, 160 (2015), arXiv:1411.5848 [gr-qc]
R. Casadio, O. Micu, F. Scardigli, Quantum hoop conjecture: Black hole formation by particle collisions. Phys. Lett. B 732, 105 (2014), arXiv:1311.5698 [hep-th]
R. Casadio, A. Giugno, O. Micu, A. Orlandi, Black holes as self-sustained quantum states, and Hawking radiation. Phys. Rev. D 90, 084040 (2014), arXiv:1405.4192 [hep-th]; R. Casadio, A. Giugno, A. Orlandi, Thermal corpuscular black holes, Phys. Rev. D 91, 124069 (2015), arXiv:1504.05356 [gr-qc]
R. Casadio, O. Micu, D. Stojkovic, Inner horizon of the quantum Reissner–Nordströ m black holes. JHEP 1505, 096 (2015), arXiv:1503.01888 [gr-qc]
R. Casadio, O. Micu, D. Stojkovic, Horizon wave-function and the quantum cosmic censorship. Phys. Lett. B 747, 68 (2015), arXiv:1503.02858 [gr-qc]
E. Poisson, W. Israel, Internal structure of black holes, Phys. Rev. D 41, 1796 (1990); V.I. Dokuchaev, Mass inflation inside black holes revisited, Class. Quantum Gravity 31, 055009 (2014), arXiv:1309.0224 [gr-qc]; E. Brown, R.B. Mann, Instability of the noncommutative geometry inspired black hole, Phys. Lett. B 694, 440 (2011), arXiv:1012.4787 [hep-th]; E.G. Brown, R.B. Mann, L. Modesto, Mass inflation in the loop black hole. Phys. Rev. D 84, 104041 (2011), arXiv:1104.3126 [gr-qc]
G. Dvali, C. Gomez, “Black holes as critical point of quantum phase transition, arXiv:1207.4059 [hep-th]; Black hole’s 1/N hair, Phys. Lett. B 719, 419 (2013), arXiv:1203.6575 [hep-th]; R. Casadio, A. Orlandi, Quantum harmonic black holes, JHEP 1308, 025 (2013), arXiv:1302.7138 [hep-th]
R. Penrose, Gravitational collapse: the role of general relativity, Riv. Nuovo Cim. 1, 252 (1969); Gen. Relativ. Gravit. 34, 1141 (2002)
Acknowledgements
We would like to thank D. Stojkovic for his contribution to the work reported here. R.C. was supported in part by the INFN grant FLAG. O.M. was supported in part by research grant UEFISCDI project PN-II-RU-TE-2011-3-0184.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2018 Springer Nature Switzerland AG
About this paper
Cite this paper
Casadio, R., Micu, O. (2018). A Quantum Cosmic Conjecture. In: Nicolini, P., Kaminski, M., Mureika, J., Bleicher, M. (eds) 2nd Karl Schwarzschild Meeting on Gravitational Physics. Springer Proceedings in Physics, vol 208. Springer, Cham. https://doi.org/10.1007/978-3-319-94256-8_14
Download citation
DOI: https://doi.org/10.1007/978-3-319-94256-8_14
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-94255-1
Online ISBN: 978-3-319-94256-8
eBook Packages: Physics and AstronomyPhysics and Astronomy (R0)