Black Hole Thermodynamics and the Random Matrix Model of Jackiw-Teitelboim Gravity

Abstract

Jackiw-Teitelboim (JT) gravity, a model of 2-D gravity coupled to a scalar “dilaton” field, has recently attracted considerable attention as a solvable model for holographic descriptions of Quantum Gravity. JT gravity describes the “near-horizon” region of a large class of black holes with symmetry in the “near-extremal” limit. This makes JT gravity a simplified model of a more complicated theory of black holes, nonetheless, it is expected that it still captures most of the interesting physics. One can study its “holographic duals,” which are quantum mechanical systems that describe the JT gravity system. It is hoped that JT gravity will offer valuable insight into how holography works to give us a microscopic, quantum mechanical picture of black hole physics and thermodynamics. This thesis has two overarching themes. First, we will present a review of the various holographic dual descriptions of JT gravity. We will motivate their study within both the historical and current context while building towards our eventual discussion of the recent discovery by Saad, Shenker and Stanford that JT gravity is dual to a type of Random Matrix Theory (RMT). However, the implications of this duality as well as a fundamental description of its origin are not currently well-understood. Thus, the second theme of this thesis is to better understand the physical interpretation of this particular RMT dual. We will discuss the implications of the duality in regards to the large conceptual questions of understanding black hole physics and thermodynamics, drawing connections to concepts such as coarse-graining and the chaotic nature of black holes.