## Abstract

We show that the Wald Noether-charge entropy is canonically conjugate to the opening angle at the horizon. Using this canonical relation, we extend the Wheeler-DeWitt equation to a Schrödinger equation in the opening angle, following Carlip and Teitelboim. We solve the equation in the semiclassical approximation by using the correspondence principle and find that the solutions are minimal uncertainty wavefunctions with a continuous spectrum for the entropy and therefore also of the area of the black hole horizon. The fact that the opening angle fluctuates away from its classical value of 2. indicates that the quantum black hole is a superposition of horizonless states. The classical geometry with a horizon serves only to evaluate quantum expectation values in the strict classical limit.

Original language | English |
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Pages (from-to) | 653-656 |

Number of pages | 4 |

Journal | Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics |

Volume | 718 |

Issue number | 2 |

DOIs | |

State | Published - 5 Dec 2012 |

### Bibliographical note

Funding Information:The research of R.B. and M.H. was supported by Israel Science Foundation grant No. 239/10 . M.H.ʼs research was supported by The Open University of Israel Research Fund . We thank Sunny Itzhaki for his help and advice, for many valuable and detailed discussions and for important and useful suggestions. We also would like thank Joey Medved for enlightening discussions.