📝 SummarXiv

Abstract

It has been established in both high and low spacetime dimensions that existing constructions of entanglement islands, at least in the study of black holes, are all in the context of massive gravity. In fact, later studies realized that the graviton mass is not an accident and it is necessary for the consistency of the holographic interpretation for entanglement islands. An important lesson we learned from these studies is that the graviton mass is a manifestation of the deep relationship between quantum entanglement and emergent geometry (EPR=ER). Nevertheless, various interesting questions and counter-arguments exist regarding whether this connection is of any relevance, either by modifying the definition of entanglement islands or denying the graviton mass as a physically relevant concept. In this paper, we will revisit the necessity of graviton mass for the consistency of entanglement islands and address the above questions in and out of the literature. Since the calculations in higher dimensions are already well understood, we will start with a demonstration of massive islands in a frequently used lower dimensional model, AdS$_{2}$ Jackiw-Teitelboim (JT) gravity coupled with transparent conformal matter fields, for which the relationship between energy dissipation and the graviton mass manifests. We will then discuss the necessity of graviton mass for entanglement islands in general situations and clarify the physical meaning of graviton mass. In the end, we will comment on the attempts to construct entanglement islands in massless gravity and suggest the search for a new type of entanglement wedges in holography. The purpose of this paper is to summarize the recent progress, clarifying potential confusions and convey key messages to both experts and non-experts in the field.