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 contributions in BTZ.
Geometric Interpretation of Timelike Entanglement Entropy,
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Conditions for boundary-anchored geodesics are derived in all branches of the quantum BTZ black hole, supporting a conjecture that photon spheres enable space-like connections between time-like separated boundary points.
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Holographic timelike entanglement and subregion complexity with scalar hair
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 contributions in BTZ.
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Photon spheres and bulk probes in $\text{AdS}_3$/$\text{CFT}_2$: the quantum BTZ black hole
Conditions for boundary-anchored geodesics are derived in all branches of the quantum BTZ black hole, supporting a conjecture that photon spheres enable space-like connections between time-like separated boundary points.