Momentum/Complexity Duality and the Black Hole Interior
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.
Keywords
Cite
@article{arxiv.1912.05996,
title = {Momentum/Complexity Duality and the Black Hole Interior},
author = {José L. F. Barbón and Javier Martín-García and Martin Sasieta},
journal= {arXiv preprint arXiv:1912.05996},
year = {2020}
}
Comments
27 pages, 6 figures