⚛️ high-energy theory

Where in the Island is the Information?

This paper argues that the quantum information contained within the black hole "island" responsible for reproducing the Page curve is not distributed throughout the interior but is instead concentrated in a tiny space-like region immediately adjacent to the event horizon at the Page time, as demonstrated by applying the covariant entropy bound and analyzing typical pure states via tensor network renormalization.

Original authors: T. Banks

Published 2026-10-05

📖 6 min read🧠 Deep dive

CC BY 4.0

Original authors: T. Banks

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

In the deepest corners of modern physics, researchers are trying to solve a puzzle that has haunted them for decades: what happens to the information inside a black hole when it evaporates? For a long time, the prevailing view suggested that as a black hole shrinks and disappears, the information about everything that fell into it simply vanishes, violating a fundamental rule of quantum mechanics that says information can never be destroyed. To explore this, physicists use a powerful idea called the "holographic principle," which suggests that the three-dimensional reality of our universe, including gravity, is actually a projection of information stored on a two-dimensional surface, much like a hologram. They also rely on a concept known as the "island formula," a mathematical tool that helps calculate how information is shared between a black hole and the radiation it emits. The central question is not just whether the information survives, but exactly where it hides inside the black hole during the process of evaporation.

A recent study by physicist Tom Banks at Rutgers University tackles this question by asking a very specific, physical question: if the information is indeed preserved in a region called the "island" inside the black hole, where exactly within that vast interior is it located? The answer, according to Banks, is far more concentrated than many had imagined. Using a combination of established rules about how entropy limits information and a method for analyzing quantum systems that looks at how they change across different scales, Banks argues that the quantum information is not spread out throughout the black hole's interior. Instead, it is packed tightly into a tiny, thin layer of space sitting just inside the black hole's event horizon.

To understand this, one must first picture the black hole as a system that is slowly losing energy. As it evaporates, a point is reached called the "Page time," where the amount of information that has escaped into the surrounding radiation equals the amount of information still trapped inside. At this moment, the "island formula" suggests that a region inside the black hole becomes entangled with the outside radiation, effectively allowing the information to be retrieved. However, if one looks at this situation using standard physics equations that describe fields in space, it creates a confusing paradox. It appears that information from deep inside the black hole, which has been cut off from the outside world for a long time, is suddenly connected to the outside. This would imply that information is traveling faster than light or appearing in places it shouldn't be able to reach.

Banks resolves this paradox by showing that the standard equations are misleading about where the information actually sits. He applies a fundamental limit on how much information can fit inside a specific region of space, known as the covariant entropy bound. When he calculates the maximum amount of information that could possibly be held by a detector falling into the black hole from various starting points, he finds a stark difference. If a detector starts anywhere deep inside the black hole, far from the edge, the amount of information it can access is tiny compared to the total information of the black hole. The only way to access the full amount of information is to be located extremely close to the horizon, the boundary of no return. In fact, the information is concentrated in a region so close to the horizon that it is only a tiny fraction of the black hole's total size away from it, yet still within the interior.

The paper supports this conclusion with a second line of reasoning that treats the black hole like a complex statistical system. By looking at how quantum states are organized in a mathematical framework known as a tensor network, which acts like a way of zooming in and out on the structure of space, Banks shows that the "typical" state of an evaporating black hole has its probability concentrated in a very narrow range of distances. Just as a specific musical note has a very specific frequency, the quantum state of the black hole is focused on a specific shell of space near the horizon. The rest of the interior, while vast, contains states that are essentially irrelevant to the specific information being tracked. This means that the "island" where the information lives is not a large, sprawling region deep in the dark, but a microscopic layer hugging the edge of the black hole from the inside.

This finding challenges earlier suggestions that the information might be spread out over a much larger area, potentially extending far outside the horizon in higher dimensions. Banks argues that such a spread would require the black hole to react violently to the presence of the information, changing its mass in ways that are not observed. Instead, the information must be confined to a region where the physics remains stable. The study suggests that as an object falls into a black hole, its information does not travel all the way to the center to hit the singularity. Rather, it quickly thermalizes, or mixes, with the degrees of freedom on the horizon itself. This process is akin to a relay race where information is passed along a chain of observers, moving from the deep interior up to the horizon, ensuring that the data is never lost but simply relocated to the boundary.

Ultimately, the paper proposes that the dramatic event of hitting the singularity is not a journey to a place where information is destroyed, but a sign that the local information has fully merged with the vast, holographic storage of the horizon. The "island" is real, but it is not the deep interior of the black hole; it is a thin, stretched membrane just inside the point of no return. This insight helps reconcile the strange behavior of black holes with the strict laws of quantum mechanics, suggesting that the universe preserves information by keeping it close to the surface, even when it appears to be lost in the depths. The work does not claim to have solved every mystery of gravity, but it provides a clear, physical picture of where the missing pieces of the puzzle are hiding, grounding the abstract mathematics of black hole evaporation in a concrete location.

Technical Summary: "Where in the Island is the Information?"

Problem Statement
The paper addresses a paradox arising from the "Island Formula" for Quantum Extremal Surfaces (QES) in the context of evaporating large Anti-de Sitter (AdS) black holes. While the Island Formula successfully reproduces the Page curve for the combined CFT/bath system, it implies that at the Page time, a region deep inside the black hole interior (the "island") becomes entangled with the external radiation. In an Effective Field Theory (EFT) description using "nice slice" coordinates, this suggests a paradoxical entanglement between degrees of freedom that have been causally disconnected from the exterior since long before the Page time. The central question is: Where exactly within the island is the quantum information concentrated? Does it reside throughout the interior volume, or is it localized?

Methodology
The author employs two primary lines of argumentation to locate the information, supplemented by a discussion on non-isometric encodings and causal propagation:

Covariant Entropy Bound (CEB) Application: The paper analyzes the causal diamonds of geodesics originating from the spatial region that becomes the island, evaluated on a time slice just prior to the Page time. By applying the covariant entropy bound, the author calculates the maximum entropy accessible to a detector within these causal diamonds.
Quantum Statistical Mechanics and Tensor Network Renormalization (TNRG): The author utilizes the TNRG framework (Evenbly and Vidal) as a regularization of the boundary CFT. This involves mapping the CFT to a sequence of lattice models on a hyperbolic space, where shell radius corresponds to energy scale (scale/radius duality). The analysis focuses on the wavefunction of a typical pure state in the microcanonical ensemble representing the black hole.
Semiclassical Back-Reaction Analysis: The paper re-examines arguments regarding "islands" extending far outside the horizon (specifically referencing Bousso and Penington) by calculating the semiclassical back-reaction of deviations from the Hartle-Hawking state on the black hole mass in large AdS space.
Hilbert Bundle and "Bucket Brigade" Formalism: The author discusses the structure of the Hilbert space as a bundle over the space of time-like geodesics and proposes a mechanism for information transfer along the Einstein-Rosen bridge.

Key Contributions and Results

Localization via Entropy Bounds: Applying the CEB to geodesics originating in the island region reveals that for any point not extremely close to the horizon, the maximal area of the causal diamond boundary is a tiny fraction of the black hole entropy. Consequently, the CEB implies that the vast majority of the quantum information in the island must be concentrated in a tiny space-like portion very close to the black hole horizon. The paper notes that the largest value of the radial coordinate for the island is $r \sim r_H - K L_P$ , where $K$ is the number of quantum fields used in computing the generalized entropy.
Wavefunction Concentration in Tensor Networks: Using TNRG, the author argues that a typical pure black hole state has its probability weight concentrated in a narrow range of energy eigenstates. Due to scale/radius duality, this narrow energy range corresponds to a small radial interval in the dual tensor network/AdS slice, specifically around the Schwarzschild radius. Shells at larger radii distribute this information among a vast number of orthogonal degrees of freedom, effectively hiding it. Thus, the wavefunction entangled with the bath lives close to the horizon, within a stretched horizon of width $\sim R_{AdS}(L_P/R_{AdS})^{(d-2)/d}$ .
Refutation of "Far Outside" Islands in AdS: The paper argues that the Bousso-Penington result (where islands extend far outside the horizon in Minkowski space) does not directly apply to large AdS black holes. A back-reaction calculation shows that for large AdS black holes, deviations from the Hartle-Hawking state must be spread over a region of size $\rho_h \sim R_{AdS}(L_P/R_{AdS})^{(d-2)/d}$ to avoid large mass shifts. This scale is larger than the Planck scale but significantly smaller than the AdS radius, and independent of the black hole radius $r_s$ .
Information "Bucket Brigade": The paper proposes that information from infalling detectors is not lost at the singularity but is transferred to the horizon via a "causal holographic bucket brigade." As a detector falls in, the maximal area of its causal diamond shrinks. However, due to the overlap of diamonds from sequential infalling detectors, information can be transferred from the interior to the horizon. This process relies on the thermalization of local degrees of freedom with holographic variables on the diamond boundaries.
Non-Isometric Encodings: The results support the view that the QFT description overcounts states. The true quantum gravity Hilbert space is encoded non-isometrically, where the "bulk" field theory is a coarse-grained description. The encounter with the singularity is interpreted as the thermalization of local degrees of freedom with the more numerous holographic q-bits located on the boundaries of causal diamonds.

Significance and Claims
The paper claims to resolve the apparent paradox of the Island Formula by demonstrating that the "island" is not a large volume of the interior, but rather a thin shell near the horizon.

Resolution of the Paradox: The information is not causally disconnected in the way EFT suggests; rather, the degrees of freedom entangled with the radiation are localized within a stretched horizon region accessible to the horizon's hydrodynamics.
Nature of Black Hole Entropy: The entropy of large AdS black holes cannot be understood microscopically in terms of bulk AdS field theory (BDHM/HKLL). Instead, it arises from "soft" or high-energy holographic states (analogous to soft supergravitons in Minkowski space) that dominate the entropy but are not captured by standard bulk EFT.
Physical Interpretation: The paper suggests that the "singularity" represents the point where local degrees of freedom equilibrate with the horizon's holographic variables. The information retrieval process is consistent with the unitary evolution of the CFT, provided one accepts that the information is concentrated near the horizon and that the bulk EFT description fails to capture the true holographic dynamics on small scales.

The author notes that while the mathematical framework (Island Formula, TNRG) provides precise answers, these answers describe an idealized, isolated system. In a realistic physical experiment involving a black hole subject to environmental influences, the state would evolve into a mixed state, and the ability to perform the complete quantum measurements required to verify these specific wavefunction properties is vanishingly small. Nevertheless, the theoretical arguments suggest that the information paradox is resolved by the localization of information near the horizon and the non-isometric nature of the encoding between the bulk and the boundary.

More like this