Subregion Action and Complexity
Abstract
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. 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 boundary gives rise to a linear time growth, while we have a classical contribution due to a timelike boundary that is given by the free energy.
Cite
@article{arxiv.1809.06031,
title = {Subregion Action and Complexity},
author = {Mohsen Alishahiha and Komeil Babaei Velni and M. Reza Mohammadi Mozaffar},
journal= {arXiv preprint arXiv:1809.06031},
year = {2019}
}
Comments
26 pages, 5 figures, v2: typos corrected, references added, v3: matches published version