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BTZ dynamics and chaos
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abstract
We find an effective action for gravitational interactions with scalars in $AdS_3$ to first order in $G_N$ at the conformal boundary. This action can be understood as an action for the Brown-Henneaux modes and is given by the square-root product of right and left moving Schwarzian derivatives for conformal transformations of the boundary. We thus reproduce the result $\lambda_L=\frac{2\pi}{\beta}$ for OTOC computed first in arXiv:1412.6087 for a Schwarzchild black hole in $AdS_3$. Applying the same procedure to rotating BTZ we find the Lyapunov index to be $\lambda_L=\frac{2\pi}{\beta_+}>\frac{2\pi}{\beta}$ where $\beta_+=\beta(1-\mu_L)$, with $\mu_L=\frac{r_-}{r_+}$ being the chemical potential for angular momentum. We thus comment on a possible modification to a part of the proof given in arXiv:1503.01409 to accommodate this result.
Forward citations
Cited by 5 Pith papers
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Cosmological pole-skipping, shock waves and quantum chaotic dynamics of de Sitter horizons
Pole-skipping in Schwarzschild-de Sitter predicts superluminal and imaginary butterfly velocities, confirmed by shock wave analysis, hinting at nonlocal and non-Hermitian dual dynamics.
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Chaos in the butterfly cone
The velocity-dependent Lyapunov exponent inside the butterfly cone satisfies λ(v) ≤ 2πT(1-|v|/v_B), a generalization of the chaos bound, saturated in SYK chains, holographic theories, and large N CFTs.
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Butterfly effect and $\textrm{T}\overline{\textrm{T}}$-deformation
For T\bar{T}-deformed BTZ black holes, the butterfly velocity is v_B = sqrt(1 - 8π² μ/β²), exceeding the Mezei-Stanford bound for μ<0 while the Lyapunov exponent stays at the maximal value 2π/β.
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Global Symmetry and Maximal Chaos
For arbitrary-high-charge operators in a system with a global symmetry and chemical potential, the chaos bound weakens to 2πT/(1-|μ/μ_c|), where μ_c is the critical chemical potential.
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A Dynamical Systems Framework for Reinforcement Learning Safety and Robustness Verification
The claimed RL safety verification framework is absent from the manuscript; the body text is an unrelated high-energy physics paper about de Sitter horizon chaos.
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