Size and momentum of an infalling particle in the black hole interior

TL;DR

This paper explores how the size and momentum of an infalling particle in a black hole interior relate to quantum circuit properties, revealing a connection between operator size growth and particle trajectory near the horizon.

Contribution

It introduces a generalized notion of operator size linked to interior particle momentum, extending previous concepts and highlighting a form of complementarity.

Findings

Operator size growth correlates with the infalling particle's trajectory.

A generalized operator size relates to both exterior and interior momentum.

The study links quantum complexity with black hole interior dynamics.

Abstract

The future interior of black holes in AdS/CFT can be described in terms of a quantum circuit. We investigate boundary quantities detecting properties of this quantum circuit. We discuss relations between operator size, quantum complexity, and the momentum of an infalling particle in the black hole interior. We argue that the trajectory of the infalling particle in the interior close to the horizon is related to the growth of operator size. The notion of size here differs slightly from the size which has previously been related to momentum of exterior particles and provides an interesting generalization. The fact that both exterior and interior momentum are related to operator size growth is a manifestation of complementarity.