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arXiv · 2509.03997

Page curves and island's delays in asymptotically flat 2d spacetimes with injections

Yuuta Saito
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Abstract

We explore spacetimes with multiple energy injections in asymptotically flat two-dimensional black hole and analyze the entanglement entropy in such spacetimes. This work is an extension of the setup of the single-injection case, by F. F. Gautason, L. Schneiderbauer, W. Sybesma and L. Thorlacius, to include the multiple energy injections. We derive the solution of the model, by J. G. Russo, L. Susskind and L. Thorlacius, for a general number $n$ of the total injections, and discuss the entropy only for the case $n=2$. The essential point of this work is in the delay of the island. This delay makes the intermediate state necessary, where the island's endpoint lies between the 1st and the 2nd injections while the observer is located after the 2nd injection. The intermediate state makes the entanglement entropy evolve continuously across the 2nd injection time.

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Yuuta Saito. 2026-02-12. Page curves and island's delays in asymptotically flat 2d spacetimes with injections. https://doi.org/10.1093/ptep%2Fptaf174

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