Holographic complexity of rotating black holes with conical deficits

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.