The Quantum Gravity Dynamics of Near Extremal Black Holes (1809.08647v3)

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.

Overview of the Paper: The Quantum Gravity Dynamics of Near Extremal Black Holes

This paper explores the quantum gravitational effects in the vicinity of near-extremal black holes by employing the dynamics of spacetime geometries near their horizons. The author, Zhenbin Yang, provides rigorously derived solutions within the framework of the Jackiw-Teitelboim (JT) model, a two-dimensional dilaton gravity model expressed in terms of an $AdS_2$ throat with a slowly varying space.

Key Components of the Study

The paper begins by describing the universal structure of near-extremal black holes, highlighting the relevance of the JT action in capturing their low-energy gravitational dynamics. The JT action, presented as the Einstein-Hilbert action augmented by matter fields, serves as the fundamental gravitational model. The insights from this paper lie in its quantization approach, where the authors focus on the dynamical properties of the boundary of $AdS_2$ space, which is fundamentally controlled by both extrinsic curvature and the SL(2, R) symmetry.

The main contributions and results can be summarized as follows:

• Exact Solutions: The paper solves the JT theory exactly by connecting the boundary dynamics to a problem resembling a non-relativistic particle in a magnetic field moving in $AdS_2$.
• Correlation Functions: The authors provide explicit formulations and numerical results for all correlation functions, taking into account quantum gravity backreaction.
• Wheeler-DeWitt (WdW) Wavefunction: The paper offers the exact Wheeler-DeWitt wavefunction in the Schwarzian limit and investigates its role in the growth of complexity within quantum gravity frameworks.
• Complexity Growth: The complexity growth, conjectured to measure the linear expansion of Einstein-Rosen bridges, is quantitatively analyzed following the exact calculation of the WdW wavefunction.

Theoretical Implications

The conclusions drawn from this paper provide concrete paths to understanding the quantum properties of black hole horizons under extreme conditions. These results have significant implications for two-dimensional quantum gravity, emphasizing how JT dynamics can be used to comprehend the emergent concepts of holography in lower-dimensional spacetime geometries.

Practical Insights

The practical utility of these findings extends towards resolving intricate questions in gravity and quantum mechanics, such as black hole thermodynamics, information paradoxes, and even the characteristics of semi-classical entropy. Moreover, the potential for applying these JT dynamics in SYK-type models offers an avenue for simulating and validating chaotic systems using quantum mechanical simulations.

Future Directions

The research lays groundwork for future advancements in the nutation of gravitational systems using exact quantization methodologies. Extending this approach to higher-dimensional theories or encompassing different matter field interactions could yield richer symmetrical treatments and insights into holography across varying dimensional contexts and scales. Further exploration of such models could refine our understanding of black holes in the primordial universe, especially in scenarios where these theoretical models intersect with observations and simulations.

Overall, this paper contributes methodologically robust insight to the field of quantum gravity, offering a quantifiable understanding of gravitational dynamics in $AdS_2$ spaces, and setting the stage for ongoing research and contemplation in the upper echelons of theoretical physics.