Black Hole Interior and Time-like Entanglement Entropy

Run-Qiu Yang; Zi-Hao Li

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Black Hole Interior and Time-like Entanglement Entropy

Zi-Hao Li, Run-Qiu Yang

High Energy Physics - Theory · Submitted 26 Jan 2026 · Published version

abstract compiled · 2026-10-06 · no language-model review

The authors' main claim These results suggest that the TEE may supply a novel boundary quantum-information measure to detect structure hidden inside the black hole and suggests a deep connection between TEE and cosmic censorship.

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We investigate the possibility of using holographic time-like entanglement entropy (TEE) to probe the black hole interior. We choose the complex-valued extremal surface mixing spatial and temporal segments as one concrete example from various holographic candidates. In Schwarzschild-AdS black holes, we demonstrate that the TEE of time-like strips in such a holographic proposal exhibits linear growth at large temporal widths, possesses a physically significant imaginary part, and obeys a time-like entanglement first-law-like relation for its real part. By analyzing charged, scalar-hairy black holes, we find this geometric TEE detects a hidden "causal phase transition" separating Type-I and Type-II interiors. We identify a critical temporal width $\tau_c$ serving as a bulk diagnostic, potentially acting as a boundary order parameter: for strips narrower than $\tau_c$, the system enters a distinct phase dominated purely by time-like contributions up to an emergent effective scale; conversely, for strips wider than $\tau_c$, space-like entanglement re-emerges. Notably, a Cauchy horizon drives $\tau_c$ to infinity, leading to a pure time-like entanglement phase. These results suggest that the TEE may supply a novel boundary quantum-information measure to detect structure hidden inside the black hole and suggests a deep connection between TEE and cosmic censorship.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#	sentence	role	the authors' own work	states the main conclusion	strength
s0	We investigate the possibility of using holographic time-like entanglement entropy (TEE) to probe the black hole interior.	contribution 0.92	0.68	0.05	hedged possibility 0.96
s1	We choose the complex-valued extremal surface mixing spatial and temporal segments as one concrete example from various holographic candidates.	method 0.90	0.82	0.03	asserted 0.93
s2	In Schwarzschild-AdS black holes, we demonstrate that the TEE of time-like strips in such a holographic proposal exhibits linear growth at large temporal widths, possesses a physically significant imaginary part, and obeys a time-like entanglement first-law-like relation for its real part.	result 1.00	0.95	0.18	asserted 1.00
s3	By analyzing charged, scalar-hairy black holes, we find this geometric TEE detects a hidden "causal phase transition" separating Type-I and Type-II interiors.	result 0.98	0.95	0.19	asserted 1.00
s4	We identify a critical temporal width $\tau_c$ serving as a bulk diagnostic, potentially acting as a boundary order parameter: for strips narrower than $\tau_c$, the system enters a distinct phase dominated purely by time-like contributions up to an emergent effective scale; conversely, for strips wider than $\tau_c$, space-like entanglement re-emerges.	result 0.97	0.93	0.19	asserted 0.52
s5	Notably, a Cauchy horizon drives $\tau_c$ to infinity, leading to a pure time-like entanglement phase.	result 0.98	0.82	0.10	asserted 1.00
s6	These results suggest that the TEE may supply a novel boundary quantum-information measure to detect structure hidden inside the black hole and suggests a deep connection between TEE and cosmic censorship.	interpretation 1.00	0.55	0.83	hedged possibility 1.00

What kind of paper the classifier reports this is: theoretical result 0.96 · evidence from proof or derivation 0.96.

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The paper

Original abstract

We investigate the possibility of using holographic time-like entanglement entropy (TEE) to probe the black hole interior. We choose the complex-valued extremal surface mixing spatial and temporal segments as one concrete example from various holographic candidates. In Schwarzschild-AdS black holes, we demonstrate that the TEE of time-like strips in such a holographic proposal exhibits linear growth at large temporal widths, possesses a physically significant imaginary part, and obeys a time-like entanglement first-law-like relation for its real part. By analyzing charged, scalar-hairy black holes, we find this geometric TEE detects a hidden "causal phase transition" separating Type-I and Type-II interiors. We identify a critical temporal width $\tau_c$ serving as a bulk diagnostic, potentially acting as a boundary order parameter: for strips narrower than $\tau_c$, the system enters a distinct phase dominated purely by time-like contributions up to an emergent effective scale; conversely, for strips wider than $\tau_c$, space-like entanglement re-emerges. Notably, a Cauchy horizon drives $\tau_c$ to infinity, leading to a pure time-like entanglement phase. These results suggest that the TEE may supply a novel boundary quantum-information measure to detect structure hidden inside the black hole and suggests a deep connection between TEE and cosmic censorship.

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References

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Cited by 3 Pith papers

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

Holographic Pseudo Entropy from the Rindler Method in AdS and Flat Space
hep-th 2026-10 conditional novelty 7.0 of 10

The timelike extremal curve giving the imaginary part of holographic timelike entanglement entropy is a geodesic between the inner and outer horizons of a rotating BTZ black hole, with length universally iπℓ.
Metric and dilaton information from high-overtone quasinormal modes of analytic Einstein-Maxwell-dilaton black holes
hep-th 2026-10 accept novelty 7.0 of 10

A neutral scalar probe with a dilaton-dependent mass profile allows high-overtone quasinormal-mode spectra to separately determine the metric exponents and the signed dilaton exponent of an Einstein–Maxwell–dilaton bl...
Timelike entanglement entropy with gravitational anomaly from complexified geometry
hep-th 2026-10 accept novelty 5.0 of 10

The timelike entanglement entropy in anomalous CFT2 is reproduced holographically via a single complex geodesic whose length and frame twist give the real and imaginary parts.

How the literature uses it

6 arXiv papers cite this in 12 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

Papers citing it · 7 sentences without a confident label

Uses its method or tool 1 paper

To compute the TEE for a specific subregion in the dual boundary CFT$_d$, we employ the Complex-valued Weak Extremal Surface (CWES) prescription [ref] .

Linear Growth of Holographic Time-like Entanglement Entropy and Kasner exponents · Setup · 1.00

Cites it as background 2 papers

In parallel, a large body of work, including [ref] , investigated geometric constructions for these quantities in which the real part is attributed to spacelike geodesic segments and the imaginary part to timelike ones, with the resulting object being a composite curve rather than a single extremal surface.

Temporal Entanglement from Twist Correlators in 2d Conformal Field Theory and Holography · Introduction · 0.94
It is closely related to pseudo-entropy and transition matrices, and has been applied to Lorentzian extremal surfaces in deformed CFTs, non-relativistic theories, black-hole and wormhole geometries, RG flows, higher-curvature theories, scalar-hair backgrounds, and evaporating black-hole setups [ref] .

Holographic Timelike Entanglement and Subregion Complexity in Localized AdS3*S3*T4 Black Holes · Introduction · 0.92

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