Subregion Action and Complexity

Understand

We evaluate finite part of the on-shell action for black brane solutions of Einstein gravity on different subregions of spacetime enclosed by null boundaries.

• These subregions include the intersection of WDW patch with past/future interior and left/right exterior for a two sided black brane.
• Identifying the on-shell action on the exterior regions with subregion complexity one finds that it obeys subadditivity condition.
• This gives an insight to define a new quantity named mutual complexity.