Black Hole Collapse in the 1/c Expansion (1603.04856v3)

Abstract: We present a first-principles CFT calculation corresponding to the spherical collapse of a shell of matter in three dimensional quantum gravity. In field theory terms, we describe the equilibration process, from early times to thermalization, of a CFT following a sudden injection of energy at time t=0. By formulating a continuum version of Zamolodchikov's monodromy method to calculate conformal blocks at large central charge c, we give a framework to compute a general class of probe observables in the collapse state, incorporating the full backreaction of matter fields on the dual geometry. This is illustrated by calculating a scalar field two-point function at time-like separation and the time-dependent entanglement entropy of an interval, both showing thermalization at late times. The results are in perfect agreement with previous gravity calculations in the AdS$_3$-Vaidya geometry. Information loss appears in the CFT as an explicit violation of unitarity in the 1/c expansion, restored by nonperturbative corrections.

• The paper describes black hole formation and thermalization using CFT calculations and the AdS/CFT correspondence.
• The study computes conformal blocks at large central charge c, showing CFT predictions align with gravity calculations in the Vaidya geometry.
• Findings offer insights into reconciling information loss paradoxes via CFT and studying thermalization in strongly correlated quantum systems.

Black Hole Collapse in the $1/c$ Expansion: A CFT Perspective

The paper "Black Hole Collapse in the $1/c$ Expansion," contributed by researchers from MIT, Cornell University, and the University of Geneva, explores the phenomenon of black hole collapse using a conformal field theory (CFT) framework. This research leverages holographic principles to address the longstanding puzzles associated with black holes and information loss.

Key Objectives and Methodology

The primary objective is to describe the dynamical process of black hole formation and subsequent thermalization through CFT calculations. This approach highlights nonperturbative aspects of three-dimensional quantum gravity, particularly focusing on information loss and recovery. By adopting the AdS/CFT correspondence, the authors illustrate the equilibration of a conformal field theory following the injection of energy—akin to the formation of black holes through the collapse of a shell of matter.

Technique and Calculations

The methodology hinges on the use of a continuum version of Zamolodchikov's monodromy method, allowing for the calculation of conformal blocks at large central charge $c$. This provides a framework to compute probe observables in the collapse state. A significant part of the analysis involves examining two-point functions and entanglement entropies, which reveal thermalization characteristics consistent with gravity calculations in the AdS$_3$-Vaidya geometry. Furthermore, the technique extends to a detailed paper of correlation functions and entanglement entropy dynamics within the collapsing black hole scenario.

Numerical Results and Claims

A pivotal aspect of the paper is the comparison of theoretical predictions from CFT calculations with previous gravity-based results. The findings affirm that the dynamic CFT state models collapsing black holes accurately, providing thermal answers that align with gravity computations in the Vaidya geometry. One noteworthy claim is that information loss, apparent through the $1/c$ expansion as a violation of unitarity, is counterbalanced by nonperturbative corrections.

Implications and Future Directions

The practical implications of this paper are manifold, including insights into gravitational collapse and the broader understanding of quantum gravity. Theoretical implications touch upon the reconciliation of information loss paradoxes in general relativity and quantum mechanics through CFT paradigms. The application of these models also offers a new lens to examine thermalization processes in quantum field theories, advancing the paper of quantum chaos and strongly correlated quantum systems.

Conclusion

In conclusion, the paper enriches the discourse on black hole physics by utilizing conformal field theory to explore information paradox resolutions. It sets a durable foundation for using holographic duality to probe quantum gravity questions, especially concerning the behavior of transient black holes. This research opens pathways for further exploration into nonperturbative phenomena and their interpretations through conformal field theories in higher dimensions.