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Horizon Quantum Mechanics: Spherically Symmetric and Rotating Sources

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.

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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.

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Correspondence to Roberto Casadio.

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This work was partly supported by INFN grant FLAG.

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Casadio, R., Giugno, A., Giusti, A. et al. Horizon Quantum Mechanics: Spherically Symmetric and Rotating Sources. Found Phys 48, 1204–1218 (2018). https://doi.org/10.1007/s10701-018-0164-1

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  • DOI: https://doi.org/10.1007/s10701-018-0164-1

Keywords

  • Quantum black holes
  • Corpuscular model
  • Rotating black holes