Cosmological and black hole islands in multi-event horizon spacetimes
Gopal Yadav, Nitin Joshi
Abstract
In this paper, we have analyzed the information paradox and its resolution using the 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 membranes) and then carry out a similar study for de-Sitter patch. In both cases, when there is no island surface, the entanglement entropy has the linear time dependence as usual, whereas in the presence of an island surface, entanglement entropy becomes 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 patches consistent with the unitary evolution of black holes. In our case, we have found that the black hole island is located inside the black hole event horizon in contrast to the universal result for eternal black holes, and the cosmological island is also located inside cosmological event horizon. Further, we have studied the ``effect of temperature'' on Page curves and found that Page curves appear at late times for low-temperature black hole/de-Sitter patch and exhibit the opposite behavior for high-temperature. This implies that ``dominance of islands'' and ``information recovery'' takes more time for low-temperature black hole/de-Sitter patch in contrast to high-temperature black hole/de-Sitter patch. We also comment on the challenges of studying the information paradox in SdS spacetime without the thermal opaque membranes.