A Generalized Momentum/Complexity Correspondence

Abstract

Holographic complexity, in the guise of the Complexity = Volume prescription, comes equipped with a natural correspondence between its rate of growth and the average infall momentum of matter in the bulk. This Momentum/Complexity correspondence can be related to an integrated version of the momentum constraint of general relativity. In this paper we propose a generalization, using the full Codazzi equations as a starting point, which successfully accounts for purely gravitational contributions to infall momentum. The proposed formula is explicitly checked in an exact pp-wave solution of the vacuum Einstein equations.

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• Sewing spacetime with Lorentzian threads: complexity and the emergence of time in quantum gravity
• Lorentzian threads as 'gatelines' and holographic complexity
• Quantum complexity in gravity, quantum field theory, and quantum information science
• Holographic Complexity of Quantum Black Holes
• General Bounds on Holographic Complexity
• Complexity and Operator Growth in Holographic 6d SCFTs
• Circuit Complexity From Supersymmetric Quantum Field Theory With Morse Function
• Random Circuits in the Black Hole Interior
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