On Some Universal Features of the Holographic Quantum Complexity of Bulk Singularities

TL;DR

This study compares two holographic complexity measures in singular bulk spacetimes, revealing universal features like decreasing complexity near singularities and highlighting differences in detailed behavior across various backgrounds.

Contribution

It provides the first comparative analysis of volume and action-based holographic complexity in singular spacetimes, identifying universal and non-universal features.

Findings

Complexity decreases towards the singularity for both definitions.

Leading terms show similar behavior in some cases, but differ across backgrounds.

Next-to-leading terms are non-universal and vary with the background and definition.

Abstract

We perform a comparative study of the time dependence of the holographic quantum complexity of some space like singular bulk gravitational backgrounds. This is done by considering the two available notions of complexity, one that relates it to the maximal spatial volume and the other that relates it to the classical action of the Wheeler-de Witt patch. We calculate and compare the leading and the next to leading terms and find some universal features. The complexity decreases towards the singularity for both definitions, for all types of singularities studied. In addition the leading terms have the same quantitative behavior for both definitions in restricted number of cases and the behaviour itself is different for different singular backgrounds. The quantitative details of the next to leading terms, such as their specific form of time dependence, are found not to be universal. They vary between the different cases and between the different bulk definitions of complexity. We also address some technical points inherent to the calculation.