Lessons from the Information Paradox

TL;DR

The paper reframes the black hole information paradox by arguing that in quantum gravity, information on a Cauchy slice is redundantly accessible near the boundary (holography of information). It shows that exponentially small corrections preserve unitarity and that the exterior can encode interior data, challenging conventional locality and the need for firewalls. It surveys Page curves, islands, and state-dependent interior reconstructions in AdS/CFT, arguing that many paradoxes dissolve when boundary data are properly accounted for. The work highlights profound implications for horizon structure, boundary-bulk duality, and the consistency of quantum gravity, while outlining open questions about state-dependent bulk reconstructions and the realism of firewall/fuzzball proposals.

Abstract

We review recent progress on the information paradox. We explain why exponentially small correlations in the radiation emitted by a black hole are sufficient to resolve the original paradox put forward by Hawking. We then describe a refinement of the paradox that makes essential reference to the black-hole interior. This analysis leads to a broadly-applicable physical principle: in a theory of quantum gravity, a copy of all the information on a Cauchy slice is also available near the boundary of the slice. This principle can be made precise and established -- under weak assumptions, and using only low-energy techniques -- in asymptotically global AdS and in four dimensional asymptotically flat spacetime. When applied to black holes, this principle tells us that the exterior of the black hole always retains a complete copy of the information in the interior. We show that accounting for this redundancy provides a resolution of the information paradox for evaporating black holes and, conversely, that ignoring this redundancy leads to paradoxes even in the absence of black holes. We relate this perspective to recent computations of the Page curve for holographic CFTs coupled to nongravitational baths. But we argue that such models may provide an inaccurate picture of the rate at which information can be extracted from evaporating black holes in asymptotically flat space. We discuss large black holes dual to typical states in AdS/CFT and the new paradoxes that arise in this setting. These paradoxes also extend to the eternal black hole. They can be resolved by assuming that the map between the boundary CFT and the black-hole interior is state dependent. We discuss the consistency of state-dependent bulk reconstructions. We conclude by examining the viability of arguments for firewalls, fuzzballs and other kinds of structure at the horizon.

Figures (34)

• Figure 1: The modes $\mathfrak{a}$ are extracted by integrating the field with the red smearing function to the right of $\mathcal{U} = 0$. The modes $\widetilde{\mathfrak{a}}$ are extracted by integrating the field with the yellow smearing function on the left. The oscillations of the smearing function tend to pile up near $\mathcal{U}=0$, and these rapid oscillations provide the most significant contribution to the integral. The smearing functions are also separated by a small amount in the $\mathcal{V}$ direction although this is not visible in the figure.
• Figure 2: If we have spherical symmetry, we can extract modes, $\mathfrak{a}$ by integrating the field along the trajectory of an expanding light shell outside a sphere, and a contracting light shell inside the sphere. The blue circle in the middle is $\mathcal{U} = 0$. The modes $\mathfrak{a}$ are obtained by smearing the field with the red smearing function whereas $\widetilde{\mathfrak{a}}$ are obtained by smearing the field with the yellow smearing function. The oscillations of both smearing functions pile up near $\mathcal{U} = 0$.
• Figure 3: A black hole formed by the collapse of infalling matter (brown). The horizon is a thick orange line. To derive the formula for Hawking radiation, we are interested in late times and in correlations of the field in the red and yellow regions marked near the horizon.
• Figure 4: A schematic Penrose diagram showing the formation of the black hole and also its evaporation. Hawking radiation emerging from the horizon is marked with black arrows. The diagram also displays a "nice slice" that runs through the interior, stays away from the singularity, and also collects a significant fraction of the Hawking radiation.
• Figure 5: In a high-dimensional Hilbert space, almost all pure states look exponentially close to the maximally mixed state. The volume occupied by atypical states (depicted by black dots) is exponentially small.