Abstract
We study the nature of the inner Cauchy horizon of a Reissner-Nordström black hole in a quantum context by means of the horizon wave-function obtained from modelling the electrically charged source as a Gaussian wave-function. Our main finding is that there are significant ranges for the black hole mass (around the Planck scale) and specific charge for which the probability of realising the inner horizon is negligible. This result suggests that any semiclassical instability one expects near the inner horizon may not occur in quantum black holes.
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References
E. Greenwood and D. Stojkovic, Quantum gravitational collapse: Non-singularity and non-locality, JHEP 06 (2008) 042 [arXiv:0802.4087] [INSPIRE].
A. Saini and D. Stojkovic, Nonlocal (but also nonsingular) physics at the last stages of gravitational collapse, Phys. Rev. D 89 (2014) 044003 [arXiv:1401.6182] [INSPIRE].
T. Vachaspati, D. Stojkovic and L.M. Krauss, Observation of incipient black holes and the information loss problem, Phys. Rev. D 76 (2007) 024005 [gr-qc/0609024] [INSPIRE].
T. Vachaspati and D. Stojkovic, Quantum radiation from quantum gravitational collapse, Phys. Lett. B 663 (2008) 107 [gr-qc/0701096] [INSPIRE].
R. Casadio, Localised particles and fuzzy horizons: A tool for probing Quantum Black Holes, arXiv:1305.3195 [INSPIRE].
R. Casadio and F. Scardigli, Horizon wave-function for single localized particles: GUP and quantum black hole decay, Eur. Phys. J. C 74 (2014) 2685 [arXiv:1306.5298] [INSPIRE].
R. Casadio, Horizons and non-local time evolution of quantum mechanical systems, Eur. Phys. J. C 75 (2015) 160 [arXiv:1411.5848] [INSPIRE].
R. Casadio, O. Micu and F. Scardigli, Quantum hoop conjecture: Black hole formation by particle collisions, Phys. Lett. B 732 (2014) 105 [arXiv:1311.5698] [INSPIRE].
R. Casadio, A. Giugno, O. Micu and A. Orlandi, Black holes as self-sustained quantum states and Hawking radiation, Phys. Rev. D 90 (2014) 084040 [arXiv:1405.4192] [INSPIRE].
G. Dvali and C. Gomez, Black Holes as Critical Point of Quantum Phase Transition, Eur. Phys. J. C 74 (2014) 2752 [arXiv:1207.4059] [INSPIRE].
G. Dvali and C. Gomez, Black Hole’s 1/N Hair, Phys. Lett. B 719 (2013) 419 [arXiv:1203.6575] [INSPIRE].
G. Dvali and C. Gomez, Landau-Ginzburg Limit of Black Hole’s Quantum Portrait: Self Similarity and Critical Exponent, Phys. Lett. B 716 (2012) 240 [arXiv:1203.3372] [INSPIRE].
G. Dvali and C. Gomez, Black Hole’s Quantum N-Portrait, Fortsch. Phys. 61 (2013) 742 [arXiv:1112.3359] [INSPIRE].
R. Casadio and A. Orlandi, Quantum Harmonic Black Holes, JHEP 08 (2013) 025 [arXiv:1302.7138] [INSPIRE].
J.E. Wang, E. Greenwood and D. Stojkovic, Schrödinger formalism, black hole horizons and singularity behavior, Phys. Rev. D 80 (2009) 124027 [arXiv:0906.3250] [INSPIRE].
E. Poisson and W. Israel, Internal structure of black holes, Phys. Rev. D 41 (1990) 1796 [INSPIRE].
V.I. Dokuchaev, Mass inflation inside black holes revisited, Class. Quant. Grav. 31 (2014) 055009 [arXiv:1309.0224] [INSPIRE].
E. Brown and R.B. Mann, Instability of the Noncommutative Geometry Inspired Black Hole, Phys. Lett. B 694 (2011) 440 [arXiv:1012.4787] [INSPIRE].
E.G. Brown, R.B. Mann and L. Modesto, Mass Inflation in the Loop Black Hole, Phys. Rev. D 84 (2011) 104041 [arXiv:1104.3126] [INSPIRE].
R. Casadio, O. Micu and D. Stojkovic, Horizon Wave-Function and the Quantum Cosmic Censorship, arXiv:1503.02858 [INSPIRE].
S. Hossenfelder, Minimal Length Scale Scenarios for Quantum Gravity, Living Rev. Rel. 16 (2013) 2 [arXiv:1203.6191] [INSPIRE].
L.N. Chang, Z. Lewis, D. Minic and T. Takeuchi, On the Minimal Length Uncertainty Relation and the Foundations of String Theory, Adv. High Energy Phys. 2011 (2011) 493514 [arXiv:1106.0068] [INSPIRE].
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ArXiv ePrint: 1503.01888
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Casadio, R., Micu, O. & Stojkovic, D. Inner horizon of the quantum Reissner-Nordström black holes. J. High Energ. Phys. 2015, 96 (2015). https://doi.org/10.1007/JHEP05(2015)096
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DOI: https://doi.org/10.1007/JHEP05(2015)096