Holographic Complexity in Vaidya Spacetimes II

TL;DR

This paper explores holographic complexity in Vaidya spacetimes with shock waves, analyzing the effects on complexity evolution and formation, and emphasizes the necessity of counterterms for accurate CA proposal results.

Contribution

It extends previous work by studying complexity in Vaidya geometries with shock waves and highlights the importance of null boundary counterterms for the CA proposal.

Findings

Demonstrates the imprint of the switchback effect in complexity evolution

Shows the necessity of null boundary counterterms for correct complexity calculations

Analyzes the complexity of formation in perturbed black hole backgrounds

Abstract

In this second part of the study initiated in arxiv:1804.07410, we investigate holographic complexity for eternal black hole backgrounds perturbed by shock waves, with both the complexity$=$action (CA) and complexity$=$volume (CV) proposals. In particular, we consider Vaidya geometries describing a thin shell of null fluid with arbitrary energy falling in from one of the boundaries of a two-sided AdS-Schwarzschild spacetime. We demonstrate how known properties of complexity, such as the switchback effect for light shocks, as well as analogous properties for heavy ones, are imprinted in the complexity of formation and in the full time evolution of complexity. Following our discussion in arxiv:1804.07410, we find that in order to obtain the expected properties of the complexity, the inclusion of a particular counterterm on the null boundaries of the Wheeler-DeWitt patch is required for the CA proposal.