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This research extends the application of operator Krylov complexity from two-dimensional models to three-dimensional Anti-de Sitter space, offering a more precise method for characterizing black hole interior expansion. The findings reveal a critical discrepancy between how state and operator complexities encode evolving black hole interiors, challenging previous geometric expectations in higher dimensions. By successfully reconstructing time-dependent surfaces within black holes using boundary theory calculations, the study advances our understanding of quantum information metrics in complex gravitational systems.

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Researchers Link Operator Complexity with Growing Black Holes

Quantum ZeitgeistAugust 24, 20263 min read

Operator Krylov complexity now extends established links between operator development and internal black hole structure into three-dimensional Anti-de Sitter space, a step beyond previous work limited to two dimensions. However, unlike expectations based on geometry, calculations reveal that Krylov spread complexity fails to demonstrate equivalent expansion under these conditions. This discrepancy suggests differing roles for how state versus operator complexities encode the evolving interiors of such systems.

Building on previous work limited to two-dimensional gravity, this research proposes a new way to characterise black hole interiors by utilising boundary theory calculations with operator Krylov complexity. The team reconstructed the time dependence of a surface within a black hole by examining correlation functions of smeared operators within what’s known as a thermofield double state, reproducing…

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