Reading Topological Hair from Black-Hole Entanglement
Abstract
Black-hole hair can affect boundary mixed-state entanglement through local stress-energy and through topological information invisible to the classical metric. We separate these channels for a Nielsen--Olesen vortex on a nonrotating BTZ black hole. A superselection theorem shows that Shannon sector entropy cancels from the Markov gap, while standard U(1) symmetry-resolved reflected entropy in a thermal U(1)k CFT is equipartitioned at leading order, excluding a universal log|n| term in the imbalance-resolved gap. We therefore define a Wilson-threaded reflected moment in a probe U(1)k Chern--Simons completion coupled to the compact vortex-flux class. In a reflected-replica sector with linking number ν, its normalised phase is 2πκpnν/k, where κ∈ℤ is the mixed topological coupling; for gcd(κν,k)=1, a discrete Fourier transform reconstructs nbmod k. The RT connectivity transition switches the specified linked contour on or off, whereas the independent scale ℓ⋆ r+/L2=1.128378… determines the direction of the vortex-induced shift of that transition. The charged-moment modulus and the ordinary Markov gap remain geometric observables and are computed from a horizon-anchored Einstein-Abelian-Higgs solution with a complete first-variation kernel including the motion of the entanglement-wedge cross-section endpoints. This phase and modulus separation distinguishes topological hair from gravitational dressing without assigning an unsupported winding-dependent entropy.
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BibTeX
@misc{ghosh2026reading,
title = {{Reading Topological Hair from Black-Hole Entanglement}},
author = {Kumar Ghosh},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.18944},
eprint = {2609.18944},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.18944},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Reading Topological Hair from Black-Hole Entanglement
AU - Kumar Ghosh
PY - 2026
DA - 2026/09/01
PB - arXiv
DO - 10.48550/arxiv.2609.18944
UR - https://arxiv.org/abs/2609.18944
AB - Black-hole hair can affect boundary mixed-state entanglement through local stress-energy and through topological information invisible to the classical metric. We separate these channels for a Nielsen--Olesen vortex on a nonrotating BTZ black hole. A superselection theorem shows that Shannon sector entropy cancels from the Markov gap, while standard U(1) symmetry-resolved reflected entropy in a thermal U(1)_k CFT is equipartitioned at leading order, excluding a universal log|n| term in the imbalance-resolved gap. We therefore define a Wilson-threaded reflected moment in a probe U(1)_k Chern--Simons completion coupled to the compact vortex-flux class. In a reflected-replica sector with linking number ν, its normalised phase is 2πκpnν/k, where κ∈ℤ is the mixed topological coupling; for gcd(κν,k)=1, a discrete Fourier transform reconstructs nbmod k. The RT connectivity transition switches the specified linked contour on or off, whereas the independent scale ℓ_⋆ r_+/L^2=1.128378… determines the direction of the vortex-induced shift of that transition. The charged-moment modulus and the ordinary Markov gap remain geometric observables and are computed from a horizon-anchored Einstein-Abelian-Higgs solution with a complete first-variation kernel including the motion of the entanglement-wedge cross-section endpoints. This phase and modulus separation distinguishes topological hair from gravitational dressing without assigning an unsupported winding-dependent entropy.
ER -