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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 these regions with subregion complexity one
finds that it obeys subadditivity condition. We will also consider certain subregion that is a
part of spacetime which could be causally connected to an operator localized behind/outside the
horizon. Taking into account all terms needed to have a diffeomorphism invariant action with
a well-defined variational principle, one observes that the main contribution that results to a
nontrivial behavior of the on-shell action comes from joint points where two lightlike boundaries
(including horizon) intersect. A spacelike boundaries give rise to a linear time growth, while we
have a classical contribution due to a timelike boundary that is given by the free energy.
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