A Timelike Quantum Focusing Conjecture

TL;DR

This paper introduces a timelike quantum focusing conjecture based on generalized complexity, linking it to energy conditions and entropy bounds in quantum gravity contexts.

Contribution

It proposes a new complexity-based quantum expansion and explores its implications for energy conditions and entropy bounds in holographic settings.

Findings

Timelike quantum focusing implies a quantum strong energy condition.

A complexity bound analogous to the covariant entropy bound is derived.

For certain complexity measures, the conjecture holds and yields significant constraints.

Abstract

Recent proposals suggest that a notion of generalized complexity, analogous to generalized entropy, may be necessary for understanding the dynamics of holographic complexity in settings where quantum effects are non-negligible, such as evaporating black holes. Beginning with a notion of generalized complexity, we introduce a complexity-based quantum expansion for timelike geodesic congruences, and investigate the consequence of a timelike quantum focusing conjecture. We find that for a suitable class of codimension-0 field theory complexity measures the timelike focusing condition implies a complexity-based quantum strong energy condition as well as a complexity bound which is analogous to the covariant entropy bound.