Information radiation in BCFT models of black holes (1910.12836v3)

Abstract: In this note, following [arXiv:1905.08255, arXiv:1905.08762, arXiv:1908.10996], we introduce and study various holographic systems which can describe evaporating black holes. The systems we consider are boundary conformal field theories for which the number of local degrees of freedom on the boundary ($c_{bdy}$) is large compared to the number of local degrees of freedom in the bulk CFT ($c_{bulk}$). We consider states where the boundary degrees of freedom on their own would describe an equilibrium black hole, but the coupling to the bulk CFT degrees of freedom allows this black hole to evaporate. The Page time for the black hole is controlled by the ratio $c_{bdy}/c_{bulk}$. Using both holographic calculations and direct CFT calculations, we study the evolution of the entanglement entropy for the subset of the radiation system (i.e. the bulk CFT) at a distance $d > a$ from the boundary. We find that the entanglement entropy for this subsystem increases until time $a + t_{Page}$ and then undergoes a phase transition after which the entanglement wedge of the radiation system includes the black hole interior. Remarkably, this occurs even if the radiation system is initially at the same temperature as the black hole so that the two are in thermal equilibrium. In this case, even though the black hole does not lose energy, it "radiates" information through interaction with the radiation system until the radiation system contains enough information to reconstruct the black hole interior.

Information Radiation in BCFT Models of Black Holes

The paper discusses the phenomena of information radiation and black hole evaporation within the framework of boundary conformal field theories (BCFT). The authors focus on holographic systems whereby the number of boundary degrees of freedom ($c_{bdy}$) significantly surpasses the number of bulk CFT degrees of freedom ($c_{bulk}$). This in-depth examination offers insights into the dynamics of entanglement entropy and the formation of black holes that retain unitarity in their evolution.

Key Findings and Contributions

1. Holographic Modeling:
   • The paper uses BCFT systems to explore black hole evaporation dynamics. Through holographic duality, the systems considered are such that black holes in equilibrium can evaporate due to the coupling with the bulk CFT degrees, with the Page time dependent on the ratio $c_{bdy}/c_{bulk}$.
2. Entanglement and Phase Transitions:
   • A central focus is the evolution of entanglement entropy, showing that it increases until a phase transition occurs. After this transition, the entanglement wedge encompasses the black hole's interior. This behavior is consistent with balancing thermal equilibrium, where the black hole does not lose energy but continues to "radiate" information.
3. Theoretical Implications:
   • This work explores the nature of black hole interiors and evaporating black holes, providing insights into their transient entanglement structures. It reinforces the view that entanglement between a black hole and its Hawking radiation leads to a smooth spacetime, thereby addressing the firewall paradox.
4. Static Case Investigations:
   • The paper specifies cases where the system remains static in terms of energy density while the entanglement entropy evolves over time, providing a unique dynamic perspective despite a thermally balanced setup.
5. Conformal Transformations:
   • Through the use of conformal transformations and replica methods, the analysis provides a deeper comprehension of how entanglement dynamics can be observed in varying frames, enhancing our understanding of holographic systems from a BCFT perspective.

Implications for Future Research

This investigation advances our grasp of how boundary change dynamics can influence bulk properties in high-dimensional quantum gravity theories. It sets the stage for refined studies into the unitary evolution of black holes, offering a framework to confront longstanding paradoxes in black hole physics, such as the loss of information and firewall phenomena. The work further emphasizes that the entanglement wedge plays a critical role in black hole information dynamics, implying that radiation systems must be considered integral to the reconstruction of the interior black hole space.

Future studies could leverage the insights and models introduced to investigate other exotic configurations and boundary tensions in BCFT settings, potentially providing a path to unravel other enigma-like behaviors in quantum gravity and string theory contexts. This paper also urges a more comprehensive exploration of holographic BCFT models, which could pave the way to new methodologies for exploring non-static energy distributions and their implications on black hole evaporation processes.

In sum, the paper serves as a pivotal step towards addressing unresolved issues in black hole information theory through the lens of BCFT and holography, presenting a platform for theoretical advancements and a deeper understanding of black hole thermodynamics and quantum mechanics.