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Causality, holography, and entanglement entropy

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After giving a brief overview of holographic entanglement entropy formulas, I will explore a curious feature they imply: when the bulk spacetime includes a black hole, the entanglement entropies often appear to depend on the spacetime geometry inside the horizon. I will ask whether this implies any loss of causality in the field theory. To answer this question, I will present a new general-relativity theorem concerning the causal structure of asymptotically AdS spacetimes, which implies an interesting relationship between bulk and boundary causal domains.