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Abstract

Double holography offers a profound understanding of the island formula by
describing a gravitational system on AdS$_d$ coupled to a conformal field
theory on $\mathbb{R}^{1,d-1}$, dual to an AdS$_{d+1}$ spacetime with an
end-of-the-world (EOW) brane. In this work, we extend the proposal in [A.
Almheiri et al. JHEP 03 (2020) 149] by considering that the dual bulk spacetime
has two EOW branes: one with a gravitational system and the other with a
thermal bath. We demonstrate an equivalence between this proposal and the wedge
holographic theory. We examine it in both Anti-de Sitter gravity and de Sitter
gravity by calculating the entanglement entropy of the Hawking radiation.
Finally, we employ the doubly holographic model to verify the formula for the
entanglement entropy in a subregion within conformally flat spacetime.