Momentum/Complexity duality and the black hole interior

Abstract

Abstract We establish a version of the Momentum/Complexity (PC) duality between the rate of operator complexity growth and an appropriately defined 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

• AdS-CFT Correspondence
• Black Holes
• Holography and condensed matter physics (AdS/CMT)