Holographic complexity of rotating black holes with conical deficits

TL;DR

This paper explores how the holographic complexity of rotating black holes with conical deficits behaves under the CA and CV conjectures, revealing violations of volume-scaling and dependencies on conical deficits.

Contribution

It provides a detailed analysis of holographic complexity for accelerating Kerr-AdS black holes, highlighting the effects of acceleration and conical deficits on complexity growth and formation.

Findings

CA complexity growth rate violates volume-scaling in large black holes.

Complexity of formation decreases with conical deficits near static limit.

Complexity of formation increases with deficits near extremal regime.

Abstract

Based on the complexity equals action (CA) and complexity equals volume (CV) conjectures, we investigate the holographic complexity of a slowly accelerating Kerr-AdS black hole in the bulk Einstein gravity theory which is dual to holographic states with rotation and conical deficits in the boundary quantum system. Upon obtaining an implicit form of the Wheeler-DeWitt patch, we evaluate the action and show that the growth rate of the CA complexity violates volume-scaling formulation in large black hole limit due to the non-trivial contribution from the not-too-small acceleration of the black hole. Moreover, in an ensemble with fixed entropy, pressure, and angular momentum, we also find that complexity of formation decreases with both the average and difference of the conical deficits on the poles when the black hole is close to the static limit but increases with the deficits when the black hole is close to the extremal regime.