In asymptotically AdS black holes with space-like singularities, late-time linear growth of time-like entanglement entropy is governed by a critical extremal surface inside the event horizon, with growth rates bounded by Kasner exponents under null and dominant energy conditions.
Timelike entanglement entropy Revisited
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abstract
We present an operator-algebraic definition for timelike entanglement entropy in QFT under a few mild postulates. This rigorously defined timelike entanglement entropy is real-valued due to the timelike tube theorem. We further demonstrate why the timelike entanglement entropy should be real-valued from both path integral argument and holography perspective.
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Timelike mutual information is positive and weak monotonicity holds for non-overlapping timelike subregions in AdS3-Vaidya holography, but the timelike strong subadditivity is violated for overlapping intervals while Araki-Lieb and subadditivity hold.
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Linear Growth of Holographic Time-like Entanglement Entropy and Kasner exponents
In asymptotically AdS black holes with space-like singularities, late-time linear growth of time-like entanglement entropy is governed by a critical extremal surface inside the event horizon, with growth rates bounded by Kasner exponents under null and dominant energy conditions.
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Entanglement inequalities for timelike intervals within dynamical holography
Timelike mutual information is positive and weak monotonicity holds for non-overlapping timelike subregions in AdS3-Vaidya holography, but the timelike strong subadditivity is violated for overlapping intervals while Araki-Lieb and subadditivity hold.