Coarse-grained holography Chaos, thermalization, and gravity

Black holes, at the classical level, are relatively simple systems characterized only by three parameters: mass, electric charge, and angular momentum. Yet, at the quantum level, they are among the most erratic systems in nature due to their ability to rapidly scramble and thermalize information. In this dissertation, we aim to understand the chaotic nature of black holes using the AdS/CFT correspondence. AdS/CFT states that gravity in Anti-de Sitter (AdS) spacetimes is described by a lower-dimensional theory without gravity known as a Conformal Field Theory (CFT). We explore how chaos and thermalization integrate into CFTs despite their rigorous constraints and consistency conditions. We also clarify and give evidence in support of a statistical description of AdS/CFT, which involves an effective –meaning incomplete, or semiclassical– theory of gravity in the bulk and a ‘coarse-grained’ CFT at the boundary. We propose that semiclassical gravity is maximally agnostic about the underlying microscopic structure of the CFT. This proposal leads to a framework that quantitatively describes the statistical nature of quantum gravity. The ideas presented in this dissertation not only deepen our knowledge of chaos and its manifestations in different physical systems, but also enhance our understanding of black holes and their role in quantum gravity.