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| Main Authors: | , |
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| Format: | Preprint |
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2026
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| Online Access: | https://arxiv.org/abs/2601.18319 |
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| _version_ | 1866917223635877888 |
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| author | Li, Zi-Hao Yang, Run-Qiu |
| author_facet | Li, Zi-Hao Yang, Run-Qiu |
| contents | We establish time-like entanglement entropy (TEE) as a novel tool to characterize the black hole interior from a single-boundary perspective. In the Schwarzschild-AdS black hole, we show that TEE of time-like boundary strips exhibits linear growth as a function of temporal width in the limit of large temporal width, and that its imaginary part carries physical significance rather than being a constant. By analyzing charged, scalar-hairy black holes, we present evidence that TEE detects a hidden "causal phase transition" separating Type-I and Type-II interiors -- distinguished by singularity structure. We identify a critical temporal width $τ_c$ that acts as the order parameter for this transition: for strips narrower than $τ_c$, the system enters a distinct "time-like entanglement phase" dominated purely by time-like contributions, up to a regulator effect; conversely, for strips wider than $τ_c$, space-like entanglement re-emerges. Notably, the existence of a Cauchy horizon drives the $τ_c$ to infinity, leading to pure time-like entanglement. 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_18319 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Black Hole Interior and Time-like Entanglement Entropy Li, Zi-Hao Yang, Run-Qiu High Energy Physics - Theory We establish time-like entanglement entropy (TEE) as a novel tool to characterize the black hole interior from a single-boundary perspective. In the Schwarzschild-AdS black hole, we show that TEE of time-like boundary strips exhibits linear growth as a function of temporal width in the limit of large temporal width, and that its imaginary part carries physical significance rather than being a constant. By analyzing charged, scalar-hairy black holes, we present evidence that TEE detects a hidden "causal phase transition" separating Type-I and Type-II interiors -- distinguished by singularity structure. We identify a critical temporal width $τ_c$ that acts as the order parameter for this transition: for strips narrower than $τ_c$, the system enters a distinct "time-like entanglement phase" dominated purely by time-like contributions, up to a regulator effect; conversely, for strips wider than $τ_c$, space-like entanglement re-emerges. Notably, the existence of a Cauchy horizon drives the $τ_c$ to infinity, leading to pure time-like entanglement. 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. |
| title | Black Hole Interior and Time-like Entanglement Entropy |
| topic | High Energy Physics - Theory |
| url | https://arxiv.org/abs/2601.18319 |