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.
Omidi,Pseudo Rényi Entanglement Entropies For an Excited State and Its Time Evolution in a 2D CFT,2309.04112
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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.