Smallest matrix black hole model in the classical limit

We study the smallest nontrivial matrix model that can be considered to be a (toy) model of a black hole. The model consists of a pair of 2×2 traceless Hermitian matrices with a commutator squared potential and an SU(2) gauge symmetry, plus an SO(2) rotation symmetry. We show that using the symmetri...

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Bibliographic Details
Published in:Physical review. D 2017-05, Vol.95 (10), Article 106004
Main Authors: Berenstein, David, Kawai, Daisuke
Format: Article
Language:English
Subjects:
Angular momentum
Black holes
Chaos theory
Critical point
Liapunov exponents
Mathematical models
Matrix methods
Symmetry
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Summary:We study the smallest nontrivial matrix model that can be considered to be a (toy) model of a black hole. The model consists of a pair of 2×2 traceless Hermitian matrices with a commutator squared potential and an SU(2) gauge symmetry, plus an SO(2) rotation symmetry. We show that using the symmetries of the system, all but two of the variables can be separated. The two variables that remain display chaos and a transition from chaos to integrability when a parameter related to an SO(2) angular momentum is tuned to a critical value. We compute the Lyapunov exponents near this transition and study the critical exponent of the Lyapunov exponents near the critical point. We compare this transition to extremal rotating black holes.
ISSN:2470-0010
2470-0029
DOI:10.1103/PhysRevD.95.106004