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Zapiski Nauchnykh Seminarov POMI, 2023, Volume 520, Pages 5–16 (Mi znsl7311)  

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
References:
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.
Funding agency Grant number
Russian Science Foundation 21-12-00020
Ministry of Science and Higher Education of the Russian Federation 075-15-2022-289
A.A. was supported by RSF Grant No. 21-12-00020, A.S. is grateful to Leonhard Euler international Mathematical Institute (grant 075-15-2022-289) for support of this work.
Received: 04.07.2023
Document Type: Article
UDC: 517
Language: English
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
Citation in format AMSBIB
\Bibitem{AndLyoSta23}
\by A.~A.~Andrianov, D.~A.~Lyozin, A.~N.~Starodubtsev
\paper The spectrum of states of Ba\~nados--Teitelboim--Zanelli black hole formed by a collapsing dust shell
\inbook Questions of quantum field theory and statistical physics. Part~29
\serial Zap. Nauchn. Sem. POMI
\yr 2023
\vol 520
\pages 5--16
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl7311}
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