A Matrix Model for Black Hole Thermalization

Abstract

We present a matrix model which is intended as a toy model of the gauge dual of an AdS black hole. In particular, it captures the key property that at infinite $N$ correlators decay to zero on long time scales, while at finite $N$ this cannot happen. The model consists of a harmonic oscillator in the adjoint which acts as a heat bath for a particle in the fundamental representation. The Schwinger-Dyson equation reduces to a closed recursion relation, which we study by various analytical and numerical methods. We discuss some implications for the information problem.

23 pages, 5 eps figures. v2: expanded discussion of model, added references. v3: slightly expanded conclusions

References in corpus (4)

• Black holes as mirrors: quantum information in random subsystems
• Information Recovery From Black Holes
• Quantization in black hole backgrounds
• Large N Reductions and Holography

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• Spin Matrix Theory: A quantum mechanical model of the AdS/CFT correspondence
• Schur-Weyl duality as an instrument of Gauge-String duality
• Quantitative approaches to information recovery from black holes
• Dynamical tachyons on fuzzy spheres
• Quantum Black Hole Formation in the BFSS Matrix Model
• Non-adiabaticity and improved back-reaction
• Time-dependent Backgrounds in String Theory and Dualities