Terminal Holographic Complexity

Understand

We introduce a quasilocal version of holographic complexity adapted to `terminal states' such as spacelike singularities.

• We use a modification of the action-complexity ansatz, restricted to the past domain of dependence of the terminal set, and study a number of examples whose symmetry permits explicit evaluation, to conclude that this quantity enjoys monotonicity properties after the addition of appropriate counterterms.
• A notion of `complexity density' can be defined for singularities by a coarse-graining procedure.
• This definition assigns finite complexity density to black hole singularities but vanishing complexity density to either generic FRW singularities or chaotic BKL singularities.