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arXiv · 2307.15698

The spectrum of states of Ba~nados-Teitelboim-Zanelli black hole formed by a collapsing dust shell

Alexander A. Andrianov·Danila Lyozin·Artem Starodubtsev
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Abstract

We perform canonical analysis of an action in which 2+1-dimensional gravity with negative cosmological constant is coupled to cylindrically symmetric dust shell. The resulting phase space is finite dimensional having geometry of SO(2; 2) group manifold. Representing the Poisson brackets by commutators results in the algebra of observables which is a quantum double D(SL(2)q). Deformation parameter q is real when the total energy of the system is below the threshold of a black hole formation, and a root of unity when it is above. Inside the black hole the spectra of the shell radius and time operator are discrete and take on a finite set of values. The Hilbert space of the black hole is thus finite-dimensional.

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Alexander A. Andrianov, Danila Lyozin, Artem Starodubtsev. 2023-07-28. The spectrum of states of Ba~nados-Teitelboim-Zanelli black hole formed by a collapsing dust shell. https://arxiv.org/abs/2307.15698

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