This preprint provides a self-contained pedagogical introduction to black hole information scrambling and quantum chaos, aimed at advanced undergraduates and beginning graduate students. It covers the derivation of Hawking temperature and Bekenstein–Hawking entropy, the gravitational butterfly effect, the Lyapunov exponent, and the saturation of the universal quantum chaos bound by black holes. Numerical estimates across eight decades of black hole mass are presented, including a verification of the universal invariant λL · t∗ = ln S. The manuscript develops an explicit analogy between black hole scrambling and all-to-all random quantum circuits, making connections to quantum information theory tangible. Three worked problems suitable for classroom or self-study use are included. Keywords: black holes, quantum chaos, information scrambling, Lyapunov exponent, fast scramblers, random quantum circuits, Sachdev–Ye–Kitaev model, pedagogical preprint Notes: Preprint; Python code reproducing results is available at https://github.com/muhnehh/blackhole-scrambling.
Muhammed Nehan (Mon,) studied this question.