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We study and construct spacetimes, dubbed planar AdS-dS-wormholes, satisfyingthe null energy condition and having two asymptotically AdS boundariesconnected through a (non-traversable) inflating wormhole. As for otherwormholes, it is natural to expect dual descriptions in terms of twodisconnected CFTs in appropriate entangled states. But for our cases certainexpected bulk entangling surfaces used by the Hubeny-Rangamani-Takayanagi (HRT)prescription to compute CFT entropy do not exist. In particular, no realcodimension-2 extremal surface can run from one end of the wormhole to theother. According to HRT, the mutual information between any two finite-sizedsubregions (one in each CFT) must then vanish at leading order in large $N$ --though the leading-order mutual information per unit area between the two CFTstaken as wholes may be nonzero. Some planar AdS-dS-wormholes also fail to haveplane-symmetric surfaces that would compute the total entropy of either CFT. Wesuggest this to remain true of less-symmetric surfaces so that the HRT entropyis ill-defined and some modified prescription is required. It may be possibleto simply extend HRT or the closely-related maximin construction by a limitingprocedure, though complex extremal surfaces could also play an important role.

A paucity of bulk entangling surfaces: AdS wormholes with de Sitter interiors