Topological shadows and complexity of islands in multiboundary wormholes

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 AdS3 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.

Islands and complexity of eternal black hole and radiation subsystems for a doubly holographic model

“…Building on the main findings, we now try to explain them in terms of our present understanding and results presented in other literature on the related issue. The jump in volume at Page time for the right brane is not new and has been previously found in [80,84,86]. It is typical for the radiation state as the islands are included in the entanglement wedge of the radiation subsystem starting from the Page time.…”

“…However, we would like to stress that the positive (negative) jump for the radiation (eternal black hole) complexity at Page time seems universal and modelindependent. More arguments on this particular direction can be found in the conclusion section of [80].…”

“…This is known as the holographic subregion complexity which has been argued to be dual to the complexity of purification for the mixed state. 2 In previous work [80], the complexity of radiation state for an evaporating black hole-radiation system was computed in a multiboundary wormhole model, and a subregion complexity curve corresponding to the entanglement curve was suggested. In this work, we compute respective volumes for a model where the entanglement curve is the Page curve for an eternal black hole.…”

“…This results in the first-order phase transition of the volume curve at Page time. This has been related to the multipartite purification complexity of the Hawking quanta in [80,87], whereas the authors of [84] have argued it to be related to the mutual complexity.…”

Information transfer with a gravitating bath

“…Most work on islands in higher dimensions [9,[12][13][14][15][16][22][23][24][25][26], as well as some of the results in lower dimensions [27][28][29][30][31][32], have been obtained in the context of the Randall-Sundrum (RS) braneworlds [33] with subcritical tension branes [34,35], also known as the Karch-Randall (KR) braneworlds. Compared to the generic RS setup, KR has several specific features.…”