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.
Skenderis, Lecture notes on holographic renormal- ization, Classical and Quantum Gravity19, 5849–5876 (2002)
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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.