Entanglement Island and Page Curve in Wedge Holography

TL;DR

This paper demonstrates that entanglement islands and the associated Page curve can exist in wedge holography with massless gravity by incorporating suitable higher derivative or DGP gravity on the branes, resolving previous controversies.

Contribution

It introduces models with massless gravity on branes that recover entanglement islands and Page curves, expanding their applicability to long-range gravity theories.

Findings

Entanglement islands disappear in initial massless wedge holography models.

Adding DGP or higher derivative gravity restores entanglement islands.

Massless entanglement islands lead to non-trivial Page curves.

Abstract

Entanglement islands play an essential role in the recent breakthrough in resolving the black hole information paradox. However, whether entanglement islands can exist in massless gravity theories is controversial. It is found that entanglement islands disappear in the initial model of wedge holography with massless gravity on the brane. As a result, the entanglement entropy of Hawking radiation becomes a time-independent constant, and there is no Page curve. In this paper, we recover massless entanglement islands in wedge holography with suitable DGP gravity or higher derivative gravity on the branes. We study two typical cases. In the first case, we consider a black hole on the strong-gravity brane and a bath on the weak-gravity brane. It is similar to the usual double holography with non-gravitational baths. In the second case, we discuss two black holes on the two branes with the same gravitational strength. We recover massless entanglement islands and non-trivial Page curves in both cases. We also argue that the entanglement island is consistent with massless gravity. Our results strongly support that entanglement islands can exist in long-range theories of gravity.