The smallest matrix black hole model in the classical limit

Abstract

We study the smallest non-trivial matrix model that can be considered to be a (toy) model of a black hole. The model consists of a pair of $2\times 2$ 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.

arXiv comment19 pages, 6 figures

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• Quantum chaos in supersymmetric quantum mechanics: an exact diagonalization study
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• Chaos from Equivariant Fields on Fuzzy $S^4$
• Improved semiclassical model for real time evaporation of Matrix black holes
• Chaotic Dynamics of the Mass Deformed ABJM Model
• Chaos from Massive Deformations of Yang-Mills Matrix Models
• Thermalization in massive deformations of Yang-Mills matrix models
• Deconfinement of classical Yang-Mills color fields in a disorder potential
• Chaos in Matrix Gauge Theories with Massive Deformations