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Paper IPM / P / 15357  


Abstract:  
We evaluate finite part of the onshell 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 welldefined variational principle, one observes that the main contribution that results to a
nontrivial behavior of the onshell 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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