Quantum mechanics of a black hole

Gilad Gour
Phys. Rev. D 61, 124007 – Published 15 May 2000
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Abstract

Beginning with Bekenstein, many authors have considered a uniformly spaced discrete quantum spectrum for the black hole horizon area. It is also believed that the huge degeneracy of these area levels corresponds to the notion of black hole entropy. Starting from these two assumptions we here infer the algebra of a Schwarzschild black hole’s observables. This algebra then serves as motivation for introducing in the system’s Hamiltonian an interaction term. The interaction contains the horizon area operator, which is a number operator, and its canonical conjugate, the phase operator. The Hawking radiation from a Schwarzschild black hole is seen to be a consequence of an area-phase interaction. Using this interaction we have reproduced the semiclassical result for the Hawking radiation power. Furthermore, we show that the initial state of the black hole determines the nature of its development. Thus, a state which is an area eigenstate describes a static eternal black hole, but a coherent state describes a radiating black hole. Hence, it is the observer’s initial knowledge or uncertainty about the horizon area which determines the evolution.

  • Received 29 June 1999

DOI:https://doi.org/10.1103/PhysRevD.61.124007

©2000 American Physical Society

Authors & Affiliations

Gilad Gour*

  • Racah Institute of Physics, Hebrew University, Givat Ram, Jerusalem 91904, Israel

  • *Email address: gour@cc.huji.ac.il

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Issue

Vol. 61, Iss. 12 — 15 June 2000

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