Cosmological and black hole islands in multi-event horizon spacetimes

TL;DR

This paper investigates the black hole information paradox in Schwarzschild de-Sitter spacetime using the island proposal, revealing how islands inside horizons lead to unitary Page curves and how temperature affects information recovery times.

Contribution

It introduces the concept of black hole and cosmological islands inside horizons in multi-event horizon spacetimes and analyzes their impact on the information paradox resolution.

Findings

Islands inside horizons lead to constant entanglement entropy and Page curves.

Temperature influences the timing of island dominance and information recovery.

Black hole and cosmological islands are located inside their respective horizons.

Abstract

In this paper, we have analyzed the information paradox and its resolution using island proposal in Schwarzschild de-Sitter black hole spacetime. First, we study the information paradox for the black hole patch by treating de-Sitter patch on both sides as a frozen background (by inserting thermal opaque membrane) and then we carry out similar study for de-Sitter patch also. In both cases, when there is no island surface then the entanglement entropy has as usual the linear time dependence whereas in the presence of an island surface entanglement entropy become constant (equal to twice of thermal entropy of black hole/de-Sitter patch). Therefore, we obtain the Page curves for the black hole and de-Sitter patch consistent with the unitary evolution of black holes. In our case, we have found that black hole island is located inside the black hole event horizon in contrast to universal result for eternal black holes and also cosmological island is located inside the cosmological event horizon. Further, we have studied the "effect of temperature" on the Page curves and found that Page curves appear at later times for low temperature black holes/de-Sitter patch and it exhibit opposite behavior for high temperature. This implies that "dominance of islands" and "information recovery" takes more time for low temperature black holes/de-Sitter patch in contrast to high temperature black holes/de-Sitter patch. We also make comments on the challenges to study the information paradox in SdS spacetime without the thermal opaque membrane.