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arXiv · 1912.05996

Momentum/Complexity Duality and the Black Hole Interior

José L. F. Barbón·Javier Martín-García·Martin Sasieta
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Abstract

We establish a version of the Momentum/Complexity (PC) duality between the rate of operator complexity growth and a radial component of bulk momentum for a test system falling into a black hole. In systems of finite entropy, our map remains valid for arbitrarily late times after scrambling. The asymptotic regime of linear complexity growth is associated to a frozen momentum in the interior of the black hole, measured with respect to a time foliation by extremal codimension-one surfaces which saturate without reaching the singularity. The detailed analysis in this paper uses the Volume-Complexity (VC) prescription and an infalling system consisting of a thin shell of dust, but the final PC duality formula should have a much wider degree of generality.

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José L. F. Barbón, Javier Martín-García, Martin Sasieta. 2019-12-12. Momentum/Complexity Duality and the Black Hole Interior. https://doi.org/10.1007/jhep07(2020)169

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