Entanglement islands in generalized two-dimensional dilaton black holes

The Fabbri--Russo model is a generalized model of a two-dimensional dilaton gravity theory with various parameters ``n'' describing various specific gravities. Particularly, the Russo--Susskind--Thorlacius gravity model fits the case n=1. In the Fabbri--Russo model, we investigate Page curves and the entanglement island. Islands are considered in eternal and evaporating black holes. Surprisingly, in any black hole, the emergence of islands causes the rise of the entanglement entropy of the radiation to decelerate after the Page time, satisfying the principle of unitarity. For eternal black holes, the fine-grained entropy reaches a saturation value that is twice the Bekenstein--Hawking entropy. For evaporating black holes, the fine-grained entropy finally reaches zero. At late times and large distance limit, the impact of the parameter ``n'' is a subleading term and is exponentially suppressed. As a result, the shape of Page curves is ``n'' independent in the leading order, which also indicates the universality of the Page curve in generalized two-dimensional models. Furthermore, we discuss the relationship between islands and firewalls. We show that the island is a better candidate than firewalls for encountering the quantum entanglement-monogamy problem. Finally, we briefly review the gravity/ensemble duality as a possible resolution to the state paradox resulting from the island formula.