Topological shadows and complexity of islands in multiboundary wormholes

TL;DR

This paper investigates the evolution of subregion complexity in multiboundary wormholes within AdS3, revealing a phase transition at the Page time linked to island inclusion, using geometric and information-theoretic methods.

Contribution

It introduces a novel analysis of subregion complexity and Page curves in multiboundary wormholes, connecting geometric volumes with information-theoretic measures during black hole evaporation.

Findings

Discontinuous jump in volume complexity at Page time.

Phase transition in complexity due to island inclusion.

Correlation between wormhole geometry and information recovery.

Abstract

Recently, remarkable progress in recovering the Page curve of an evaporating black hole (BH) in Jackiw-Teitelboim gravity has been achieved through use of Quantum Extremal surfaces (QES). Multi-boundary Wormhole (MbW) models have been crucial in parallel model building in three dimensions. Motivated by this we here use the latter models to compute the subregion complexity of the Hawking quanta of the evaporating BH in AdS$_{3}$ and obtain the Page curve associated with this information theoretic measure. We use three- and $n$-boundary wormhole constructions to elucidate our computations of volumes below the Hubeny-Rangamani-Takayanagi (HRT) surfaces at different times. Time is represented by the growing length of the throat horizons corresponding to smaller exits of the multi-boundary wormhole and the evaporating bigger exit shrinks with evolving time. We track the change in choice of HRT surfaces with time and plot the volume with time. The smooth transition of Page curve is realized by a discontinuous jump at Page time in volume subregion complexity plots and the usual Page transition is realized as a phase transition due to the inclusion of the island in this context. We discuss mathematical intricacies and physical insights regarding the inclusion of the extra volume at Page time. The analysis is backed by calculations and lessons from kinematic space and tensor networks.