Holographic complexity of rotating black holes

TL;DR

This paper investigates the holographic complexity of rotating black holes, revealing connections to thermodynamic volume and analyzing growth rates that often violate Lloyd's bound, within the frameworks of 'complexity equals action' and 'complexity equals volume' conjectures.

Contribution

It provides new insights into the complexity of rotating black holes, especially relating complexity of formation to thermodynamic volume and examining late-time growth behavior.

Findings

Complexity of formation linked to thermodynamic volume for large black holes.

Late-time growth rate approaches a constant, often violating Lloyd's bound.

Simplifications occur for odd-dimensional equal-spinning black holes.

Abstract

Within the framework of the "complexity equals action" and "complexity equals volume" conjectures, we study the properties of holographic complexity for rotating black holes. We focus on a class of odd-dimensional equal-spinning black holes for which considerable simplification occurs. We study the complexity of formation, uncovering a direct connection between complexity of formation and thermodynamic volume for large black holes. We consider also the growth-rate of complexity, finding that at late-times the rate of growth approaches a constant, but that Lloyd's bound is generically violated.