Terminal Holographic Complexity

TL;DR

This paper develops a quasilocal holographic complexity measure for terminal states like spacelike singularities, demonstrating its monotonicity and defining a complexity density that varies across different singularity types.

Contribution

It introduces a new holographic complexity framework for terminal states, including a coarse-grained complexity density, with explicit examples and monotonicity properties.

Findings

Complexity density is finite for black hole singularities.

Vanishing complexity density for generic FRW and BKL singularities.

Monotonicity properties hold after adding counterterms.

Abstract

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. We comment on the similarities and differences with Penrose's Weyl curvature criterion.