Entanglement island and Page curve in wedge holography

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.

Information transfer with a gravitating bath

“…Recent work [58][59][60] has claimed that one may get nontrivial Page curves and islands even with a gravitating bath (and thus, massless gravity) by turning on brane-localized couplings-particularly DGP terms (1.2)-treated as higher-derivative corrections to RS terms (1.1). Such a result requires that the coupling G b in (1.2) be negative on at least one of the branes, but this alone is not necessarily an unphysical assumption for AdS branes.…”

Entropy of Radiation with Dynamical Gravity

“…In recent work it was discussed that the DGP terms may solve the issue of massive gravity in island models [102,103]. In this note we have seen how the parameter space is confined in order for islands to exist.…”

“…Since we are using the same model, this note and all computations and results presented here have the same feature. We remark that in [102,103] the authors claim they're able to reproduce the Page curve evolution in massless gravity. Now that we have seen the general idea of coupling a gravitating region to a nongravitating bath and the three equivalent descriptions that holography provides, it is time to include the black string.…”

“…In lower dimensions this was achieved by including JT gravity on the brane [18]. In higher dimensions we can mimic this by including an Einstein-Hilbert term in the brane action similar to Dvali-Gabadadze-Porrati (DGP) gravity in an AdS background; this was already done for empty AdS [100], for topological black holes [101] and for the wedge black string model [102][103][104]. This opens a new parameter that our theory depends on, extending our previous result.…”

“…In particular, [102,103] assert that for some part of parameter space, the wedge holographic model does reproduce the Page curve, while maintaining the massless graviton. Although we do not study this model here, we refer the reader to future work [105].…”