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Timelike Holographic Complexity

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arxiv 2510.25700 v4 pith:A4MQOCYH submitted 2025-10-29 hep-th

Timelike Holographic Complexity

Mohsen Alishahiha This is my paper
classification hep-th
keywords complexitytimelikeholographiclorentzianblackbranegeometricpseudo-entropy
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved
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Motivated by the pseudo-entropy program, we study timelike subregion complexity within the holographic Complexity-equal-Volume framework, extending previous spatial constructions to Lorentzian boundary intervals. For hyperbolic timelike regions in pure AdS, we compute the enclosed bulk volume and show that, despite the Lorentzian embedding, the resulting complexity is purely real. We generalize the analysis to AdS black brane geometries, where extremal surfaces may either remain entirely outside the horizon or penetrate it, placing their timelike branch inside the black brane interior. In both configurations, the complexity exhibits the same universal UV divergences as the spacelike case, yet it receives no imaginary contribution, highlighting its causal and geometric origin. This reality stands in sharp contrast to the complex-valued pseudo-entropy and indicates that holographic complexity retains a genuinely geometric, real character even under Lorentzian continuation.

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Cited by 6 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. Linear Growth of Holographic Time-like Entanglement Entropy and Kasner exponents

    hep-th 2026-06 conditional novelty 6.5

    Late-time linear growth of holographic TEE is governed by an interior critical surface Ac whose existence is guaranteed by NEC under Kasner asymptotics, with vacuum maximizing real growth and minimizing imaginary part.

  2. Holographic timelike complexity for de Sitter

    hep-th 2026-07 conditional novelty 6.0

    Timelike subregion volume complexity in de Sitter grows exponentially early and diverges hyperfast at a maximal duration; near the SdS black hole horizon the divergence is replaced by slower, claimed-nonlinear growth.

  3. Linear Growth of Holographic Time-like Entanglement Entropy and Kasner exponents

    hep-th 2026-06 unverdicted novelty 5.0

    Late-time TEE growth in asymptotically AdS black holes with space-like singularities is governed by a critical extremal surface inside the horizon, with real/imaginary growth rates bounded by Schwarzschild-AdS under e...

  4. Linear Growth of Holographic Time-like Entanglement Entropy and Kasner exponents

    hep-th 2026-06 unverdicted novelty 5.0

    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...

  5. Holographic complexity of conformal fields in global de Sitter spacetime

    hep-th 2026-04 unverdicted novelty 5.0

    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.

  6. Holographic timelike entanglement and subregion complexity with scalar hair

    hep-th 2026-01 unverdicted novelty 5.0

    Scalar hair breaks the time-independence of imaginary HTEE, introduces nontrivial Δt dependence, causes analytic continuation to fail, and makes timelike subregion complexity real-valued with interior-only UV-finite c...