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On black hole interior reconstruction, singularities and the emergence of time
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We propose a CFT definition of local observables in both the exterior and interior of bulk black holes, whenever such an interior exists. We achieve this by introducing a small microcanonical black hole as a "probe" and using its modular flow to propagate operators from the asymptotic boundary to the interior of other black holes along its worldline, elaborating on the ideas of [2009.04476]. The key conceptual advance is a CFT criterion for selecting states whose modular flow acts as geometric proper time translation in the bulk, which we dub "local equilibrium" states. Our interior reconstruction depends on the choice of code subspace but not on the specific black hole microstate and does not suffer from the "frozen vacuum" problem of other approaches. By virtue of our construction, the question of firewall typicality reduces to a technical problem we articulate and we identify a CFT correlator that is expected to signal the approach to the black hole singularity via a universal divergence. We end with comments on the utility of our framework to the quest for a quantum description of de Sitter cosmologies.
Forward citations
Cited by 8 Pith papers
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Uniqueness of null-local modular flow
For the free massless scalar in a Minkowski causal diamond, the vacuum is the unique state or weight in the vacuum sector whose modular flow is local on the null boundary.
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JT gravity on the worldline
Coupling a worldline observer to JT gravity replaces its evolution operator by an exactly computed average over fluctuating Euclidean times; the fluctuations are small in the disk but large on the double trumpet.
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Falling through the horizon of a quantum black hole
Gravitational dressing in JT gravity lets an infalling Unruh-DeWitt detector detect the horizon location and temperature locally, violating the equivalence principle without a firewall.
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Composite AdS geodesics for CFT correlators and timelike entanglement entropy
A bulk extremization prescription produces composite timelike-spacelike geodesics whose complex length exactly matches CFT two-point functions at timelike separation, including behind the BTZ horizon.
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A quantum algorithm for modular flow
A QSVT-based algorithm implements modular flow of an operator with respect to a density matrix in O~(κ²|t|log(κ²/ε)) queries to a block encoding of the state.
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The Baby Universe is Fine and the CFT Knows It: On Holography for Closed Universes
A closed universe in AdS/CFT is not ruled out by recent SWAP-test arguments; the one-dimensional Hilbert space seen from the CFT is external indistinguishability, and CFT data can reconstruct the closed universe's geometry.
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Comments on firewalls in JT gravity with matter
A twist factor cutoff from eigenvalue branes reproduces the gray hole firewall probabilities in JT gravity, with matter loop corrections subleading at late times.
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Correlation functions of von Neumann entropy
Two-point correlators of modular Hamiltonians obey entropy-like properties and equal the stress-tensor conformal block for spherical regions in CFT, including imaginary-time separations.
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