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Zapiski Nauchnykh Seminarov POMI, 2023, Volume 520, Pages 5–16
(Mi znsl7311)
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The spectrum of states of Bañados–Teitelboim–Zanelli black hole formed by a collapsing dust shell
A. A. Andrianova, D. A. Lyozina, A. N. Starodubtsevab a St.Petersburg State University, St.Petersburg, Russia
b Leonard Euler International Mathematical Institute, St.Petersburg, Russia
Abstract:
We perform the canonical analysis of an action $l = 0,\ldots, N$, $ n = -N,\ldots, - l, l,\ldots, N$, in which $2+1$-dimensional gravity with a negative cosmological constant is coupled to a 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 $D(\mathrm{SL}(2)_q)$. 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.
Key words and phrases:
quantum gravity, Bañados–Teitelboim–Zanelli black hole, quantum double.
Received: 04.07.2023
Citation:
A. A. Andrianov, D. A. Lyozin, A. N. Starodubtsev, “The spectrum of states of Bañados–Teitelboim–Zanelli black hole formed by a collapsing dust shell”, Questions of quantum field theory and statistical physics. Part 29, Zap. Nauchn. Sem. POMI, 520, POMI, St. Petersburg, 2023, 5–16
Linking options:
https://www.mathnet.ru/eng/znsl7311 https://www.mathnet.ru/eng/znsl/v520/p5
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Abstract page: | 41 | Full-text PDF : | 12 | References: | 17 |
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