Abstract
A quantum extremal island suggests that a region of spacetime is encoded in the quantum state of another system, like the encoding of the black hole interior in Hawking radiation. We study conditions for islands to appear in general spacetimes, with or without black holes. They must violate Bekenstein’s area bound in a precise sense, and the boundary of an island must satisfy several other information-theoretic inequalities. These conditions combine to impose very strong restrictions, which we apply to cosmological models. We find several examples of islands in crunching universes. In particular, in the four-dimensional FRW cosmology with radiation and a negative cosmological constant, there is an island near the turning point when the geometry begins to recollapse. In a two-dimensional model of JT gravity in de Sitter spacetime, there are islands inside crunches that are encoded at future infinity or inside bubbles of Minkowski spacetime. Finally, we discuss simple tensor network toy models for islands in cosmology and black holes.
Highlights
The holographic principle suggests that the entropy of a region in quantum gravity is bounded by its area in Planck units, Area S≤ (1.1)For a static, spherically symmetric matter distribution, this follows from the Bekenstein energy bound S ≤ 2πRM and the threshold for black hole collapse, M < Area/(8πR) [1]
In the four-dimensional FRW cosmology with radiation and a negative cosmological constant, there is an island near the turning point when the geometry begins to recollapse
The general conditions and most of our methods for FRW apply to regions of any shape
Summary
The holographic principle suggests that the entropy of a region in quantum gravity is bounded by its area in Planck units, Area. This suggests an interpretation of cosmological islands as a version of holographic duality where the island region is encoded in the quantum state of this auxiliary system. One of our main observations is that the three conditions together are so strong that for practical purposes they are nearly sufficient to identify the islands in a given spacetime These criteria depend only on the island region and its immediate surroundings — they make no reference to the choice of auxiliary region. We discuss the requirement that islands must maximize the generalized entropy in all timelike directions, check the conditions in some previous examples of quantum extremal islands, and discuss the relation to the Bousso bound. The tensor network model incorporates the fact that islands must violate the area bound but does not seem to capture the extremality condition or the quantum normal conditions in a natural way
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