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The Quantum Gravity Dynamics of Near Extremal Black Holes

Zhenbin Yang

TL;DR

The paper advances a complete quantum-gravity treatment of near-extremal black holes by recasting JT gravity as boundary dynamics of a particle in AdS_2 with a constant electric field. It derives an exact representation for gravity-dressed correlators (Gravitational Feynman Diagrams) and furnishes the exact Wheeler-DeWitt wavefunction in the Schwarzian limit, enabling precise analysis of ERB growth and complexity. The results show that gravitational backreaction regularizes correlators, yields a well-defined density of states, and preserves linear complexity growth of the ERB, providing a concrete test of holographic conjectures in a tractable 2D setting. Connections to SYK-like models are highlighted, offering a bridge between microscopic chaotic dynamics and macroscopic gravitational observables.

Abstract

We study the quantum effects of Near-Extremal black holes near their horizons. The gravitational dynamics in such backgrounds are closely connected to a particle in $AdS_2$ with constant electric field. We use this picture to solve the theory exactly. We will give a formula to calculate all correlation functions with quantum gravity backreactions as well as the exact Wheeler-DeWitt wavefunction. Using the WdW wavefunction, we investigate the complexity growth in quantum gravity.

The Quantum Gravity Dynamics of Near Extremal Black Holes

TL;DR

The paper advances a complete quantum-gravity treatment of near-extremal black holes by recasting JT gravity as boundary dynamics of a particle in AdS_2 with a constant electric field. It derives an exact representation for gravity-dressed correlators (Gravitational Feynman Diagrams) and furnishes the exact Wheeler-DeWitt wavefunction in the Schwarzian limit, enabling precise analysis of ERB growth and complexity. The results show that gravitational backreaction regularizes correlators, yields a well-defined density of states, and preserves linear complexity growth of the ERB, providing a concrete test of holographic conjectures in a tractable 2D setting. Connections to SYK-like models are highlighted, offering a bridge between microscopic chaotic dynamics and macroscopic gravitational observables.

Abstract

We study the quantum effects of Near-Extremal black holes near their horizons. The gravitational dynamics in such backgrounds are closely connected to a particle in with constant electric field. We use this picture to solve the theory exactly. We will give a formula to calculate all correlation functions with quantum gravity backreactions as well as the exact Wheeler-DeWitt wavefunction. Using the WdW wavefunction, we investigate the complexity growth in quantum gravity.

Paper Structure

This paper contains 22 sections, 115 equations, 10 figures.

Table of Contents

  1. Introduction
  2. Classical Solutions
  3. Charged Particle in $AdS_2$
  4. Solving the Quantum Mechanical Problem
  5. The Propagator
  6. Partition Function
  7. Quantum Gravity at Schwarzian Limit
  8. The Propagator
  9. Wheeler-DeWitt Wavefunction
  10. Correlation Functions in Quantum Gravity
  11. Gravitational Feynman Diagram
  12. Two Point Function
  13. ETH and the KMS condition
  14. Three Point Function
  15. Einstein-Rosen Bridge
  16. ...and 7 more sections

Figures (10)

  • Figure 1: Free Energy diagram with inverse temperature $\beta$.
  • Figure 2: Density of States and the Two Instantons configuration
  • Figure 3: The singular "phase" for different ordering and the geometric representation of the propagator
  • Figure 4: Classical Geometry in $\ell$ and $S$ basis
  • Figure 5: Euclidean geometries with different cusps.
  • ...and 5 more figures