In the AdS3 Vaidya geometry, the extremal volume defining holographic subregion complexity is genuinely x-dependent during the quench, so the standard x-independent ansatz fails at intermediate times; early and late time approximations are derived.
A Note on Subregion Holographic Complexity
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The volume inside a Ryu-Takayanagi surface has been conjectured to be related to the complexity of subregions of the boundary field theory. Here, we study the behaviour of this volume analytically, when the entangling surface has a strip geometry. We perform systematic expansions in the low and high temperature regimes for AdS-Schwarzschild and RN-AdS black holes. In the latter regime, we point out spurious divergences that might occur due to the limitations of a near horizon expansion. A similar analysis is performed for extremal black holes, and at large charge, we find that there might be some new features of the volume as compared to the area. Finally, we numerically study a four dimensional RN-AdS black hole in global AdS, the entangling surface being a sphere. We find that the holographic complexity captures essentially the same information as the entanglement entropy, as far as phase transitions are concerned.
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On volume subregion complexity in Vaidya spacetime
In the AdS3 Vaidya geometry, the extremal volume defining holographic subregion complexity is genuinely x-dependent during the quench, so the standard x-independent ansatz fails at intermediate times; early and late time approximations are derived.