A Reverse Black Hole Information Problem

TL;DR

The paper investigates how semiclassical AdS gravity and black hole evaporation emerge from the unitary dynamics of a boundary CFT, focusing on Lorentzian, dynamical processes. It constructs exact CFT states that model small AdS black hole formation and evaporation via trans-Planckian bulk particle collisions and analyzes boundary probes to distinguish BHs from radiation. A central theme is coarse-graining: replacing inaccessible UV data (OPE data, Hamiltonians, or time windows) with ensemble averages to reproduce the bulk’s mixed Hawking radiation while maintaining boundary unitarity; several schemes are explored, including OPE-coefficient averaging, Haar averages over Hamiltonians, and time-window averaging, with replica-wormhole considerations linking coarse-graining to unitarity restoration. The work highlights the nuanced connection between microcanonical sectors (integrable vs chaotic), the role of internal dimensions, and the potential relevance of partially deconfined states for small, evaporating black holes. It also outlines multiple refinements and future directions to better capture the relevant timescales and boundary signals of black hole dynamics in AdS/CFT.

Abstract

We study the formation, detection and coarse-graining of black holes in AdS/CFT, with an emphasis on the tension between boundary unitarity and the production of mixed state Hawking radiation in the bulk. We construct CFT states dual to black hole formation and evaporation by colliding bulk particle wavepackets at trans-Planckian energy. We propose boundary probes which are able to distinguish small AdS black holes from other states within the microcanonical ensemble. We investigate different coarse-graining prescriptions acting on the evolving CFT state, including averaging over CFT data, Hamiltonians and time windows, and compare their purities to those expected from the bulk semiclassical description. Our results clarify how semiclassical black hole behaviour can arise from an ensemble-averaging of the exact unitary dynamics, and take a step towards a better understanding of coarse-graining in the single-sided black hole information problem.

Figures (15)

• Figure 1: The mass hierarchy of black holes in AdS$_3 \times S^3$ and the corresponding operator dimensions in the 2d D1-D5 CFT. $\Delta = M \ell_{\rm AdS}$, where $M$ is the difference in ADM masses between the black hole and vacuum solutions. The black holes with mass $M \ell_{\rm AdS} \ll c$ are 6d (localised on the $S^3$) with an $S^4$ horizon topology.
• Figure 2: The mass hierarchy of black holes in AdS$_5 \times S^5$ and the corresponding operator dimensions in the 4d $\mathcal{N}=4$ SYM CFT. $\Delta = M \ell_{\rm AdS}$, where $M$ is the ADM mass. The black holes with mass $M \ell_{\rm AdS} \ll N^2$ are 10d with an $S^8$ horizon topology.
• Figure 3: The creation of a small AdS black hole by colliding two particles. The operators inserted on the boundary have a finely-tuned smearing so that the bulk particle wavepackets are beams that are localised and stay localised until they collide. Black holes that are thermodynamically unstable can be short or long-lived in AdS units; the black hole depicted is short-lived, which is why the Hawking radiation is a spherical shell (the grey cone).
• Figure 4: The mass function $h(r)$ for the thermal gas from \ref{['eq: therm sol']}, plotted for $3 \leq d \leq 9$. In all dimensions, the mass function equals zero at $r=0$ and one as $r\to \infty$. The mass function at fixed radius $r$ decreases as the dimension $d$ increases.
• Figure 5: Left: The creation of a small, unstable AdS black hole from a pure initial state, such as a collapsing star or two colliding particles. Semiclassically, the black hole emits Hawking radiation and eventually evaporates away to leave behind a mixed state of thermal radiation. Right: The expected entropy curve of the semiclassical bulk state reduced to the region outside the horizon. It rises rapidly when the horizon forms, and continues to increase while the Hawking radiation is emitted.