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.
Holographic timelike entanglement and subregion complexity with scalar hair
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abstract
We investigate the holographic timelike entanglement entropy (HTEE) and timelike subregion complexity of a thermal CFT$_d$ deformed by a relevant scalar operator $\phi_0$, dual to a hairy black hole in AdS$_{d+1}$. We employ the prescription of merging spacelike and timelike surfaces at the interior, constructing an extremal surface homologous to a boundary timelike subsystem with a time interval $\Delta t$. Consequently, this deformation breaks the invariance of the imaginary component of HTEE observed in pure AdS$_3$ and BTZ geometry, introducing a nontrivial dependence on $\Delta t$. At small $\Delta t$, we derive analytical expressions that are in agreement with numerical results, and observe partial consistency with analytic continuation to temporal or spacelike entanglement entropy at the level of the near-boundary expansion. However, analytic continuation of CFT temporal entanglement entropy fails to reproduce the HTEE calculations under boundary deformation, even in $d=2$. Furthermore, we extend the numerical calculations to higher dimensions ($d=3$). In addition, we study holographic timelike subregion complexity within the complexity=volume conjecture and find that it remains real-valued, providing a complementary geometric probe of the black hole interior. In particular, for the BTZ black hole, we analytically show that the UV-finite term of the subregion complexity receives its entire contribution from the interior region alone.
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Holographic complexity of CFTs in global dS_d is computed via volume and action prescriptions in AdS foliation and brane setups, then compared to results from static and Poincare patches.
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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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Holographic complexity of conformal fields in global de Sitter spacetime
Holographic complexity of CFTs in global dS_d is computed via volume and action prescriptions in AdS foliation and brane setups, then compared to results from static and Poincare patches.