Islands and Icebergs may contribute nothing to the Page curve

TL;DR

This paper investigates the entanglement entropy in a boundary CFT setup and finds that islands and icebergs do not contribute to the Page curve, challenging their physical relevance in entropy calculations.

Contribution

It demonstrates that islands and icebergs are inseparable and do not affect the physical Page curve, simplifying the entropy formula in AdS/CFT contexts.

Findings

Islands and icebergs contribute nothing to the Page curve.

The entropy formula reduces to the minimum of S[A] and S[B].

Islands and icebergs only affect unphysical entropy branches.

Abstract

We study the entanglement entropy of a subsystem in contact with symmetrical bath where the complete system lives on the boundary of AdS3 spacetime. The system-A is taken to be in the middle of the bath system-B and the full system is taken to be some fixed localized region of the boundary 2-dimensional CFT. We generally assume that the d.o.f.s in the total system remain fixed when we vary the size of the bath which is to be guided by the conservation laws. It is found that the island and the subleading (icebergs) contributions are inseparable, and in totality they contribute nothing to the Page-curve of the radiation. As such they contribute only to the unphysical branch of the entropy. The entropy formula of the radiation may simply be written as minimum of {S[A],S[B]} including for the black holes.