Black holes and the butterfly effect (1306.0622v3)

Abstract: We use holography to study sensitive dependence on initial conditions in strongly coupled field theories. Specifically, we mildly perturb a thermofield double state by adding a small number of quanta on one side. If these quanta are released a scrambling time in the past, they destroy the local two-sided correlations present in the unperturbed state. The corresponding bulk geometry is a two-sided AdS black hole, and the key effect is the blueshift of the early infalling quanta relative to the $t = 0$ slice, creating a shock wave. We comment on string- and Planck-scale corrections to this setup, and discuss points that may be relevant to the firewall controversy.

• The paper reveals that early-time perturbations trigger significant entanglement disruption in black holes, with scrambling occurring on a timescale t ~ β log S.
• It employs shock wave analysis within the AdS/CFT framework to demonstrate how quantum chaos rapidly drives thermalization and information scrambling.
• The study also addresses the firewall controversy by exploring string- and Planck-scale corrections that may alter classical black hole interior dynamics.

Analyzing Early-Time Perturbations and Their Impact on Correlated Entanglements in Black Holes

The paper by Shenker and Stanford provides a detailed examination of the chaotic behavior of strongly coupled quantum systems using holographic principles, particularly focusing on black hole physics and the butterfly effect. The authors leverage the AdS/CFT correspondence to explore the sensitive dependence of initial conditions in such systems, shedding light on the intersection between entanglement and thermalization in the context of quantum chaos.

The research considers thermofield double states, which provide a framework to paper finite-temperature systems through the AdS/CFT duality. By introducing mild perturbations on one side of this state, the paper analyzes how such changes propagate and affect entanglement, ultimately disrupting the bilateral correlations present initially. To contextualize these findings, the authors employ the concept of mutual information, which quantifies the extent of correlation between two subsystems.

Central to this analysis is the usage of the AdS black hole geometry, wherein the perturbation is represented as a shock wave traveling along the horizon. This results from the blueshift of the infalling quanta and illustrates how small perturbations can have macroscopic implications, aligning with the notion of scrambling -- an inherent feature of chaotic systems that efficiently obfuscates the original state information.

The paper finds that, temporal constraints notwithstanding, perturbations made at a scrambling time prior lead to significant disturbances in entanglement. This is primarily highlighted in the case of large eternal AdS Schwarzschild black holes. Quantitatively, the scrambling time aligns with $t \sim \beta \log S$, where $S$ denotes the system's entropy. This aligns with the hypothesis that black holes are among the fastest scramblers, suggesting that they excel in converting initial states into thermal distributions swiftly, thereby disrupting local entanglement.

Additionally, the paper also engages with the contemporary firewall controversy, addressing the possible implications of string- and Planck-scale corrections. The perturbative approaches, especially within the shock wave description, serve as a pivotal discussion point on how these quantum gravity corrections might manipulate the classical geometry, thereby influencing our understanding of the black hole interior.

The theoretical implications of this work are vast, suggesting a nuanced update on how we view quantum chaos and information loss within black holes. Practically, it emphasizes the robustness of the AdS/CFT framework in elucidating complex quantum phenomena. Looking forward, these findings may foster advanced inquiries into scrambling dynamics and their broader implications in quantum information science.

Furthermore, future research could explore the non-equilibrium dynamics of strongly coupled systems, advancing the work by possibly incorporating more intricate geometrical and topological properties. This could unravel deeper insights into the nature of quantum entanglements in higher-dimensional and varied topological spaces.

In summary, the paper is a substantive step in unraveling the interplay between quantum entanglement and chaos, offering valuable insights into black hole thermodynamics and the potential implications on longstanding theoretical physics debates.