Cloudy black-hole configurations of the composed Einstein-Yang-Mills-Higgs field theory: Analytic treatment
Abstract
Non-Abelian black holes that violate the non-hair conjecture are known to exist in the Einstein-Yang-Mills-Higgs field theory. The onset of hair formation in this composed physical system is marked by the presence of `cloudy' black-hole spacetimes, magnetically charged Reissner-Nordström black holes that support spatially regular linearized field configurations. In the present paper we explore, using {\it analytical} techniques, the physical and mathematical properties of the composed black-hole-linearized-field bound-state configurations of the Einstein-Yang-Mills-Higgs theory. In particular, we derive a remarkably compact analytical formula for the discrete resonance spectrum {μk}k=∞k=1 of the dimensionless mass-radius parameter μ≡ mw r+ that characterizes the cloudy black-hole-field configurations in the regime 1≪ r+≪ m−1w of small-mass weakly-magnetized black holes (here r+ is the horizon radius of the central supporting black hole and mw is the mass of the Yang-Mills field due to the Higgs effect). Interestingly, our results reveal that the excited black-hole-field resonances are characterized by the asymptotic k-independent dimensionless ratio μk+1/μk=e−2π/√3.
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BibTeX
@misc{hod2026cloudy,
title = {{Cloudy black-hole configurations of the composed Einstein-Yang-Mills-Higgs field theory: Analytic treatment}},
author = {Shahar Hod},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.02656},
eprint = {2611.02656},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.02656},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Cloudy black-hole configurations of the composed Einstein-Yang-Mills-Higgs field theory: Analytic treatment
AU - Shahar Hod
PY - 2026
DA - 2026/11/02
PB - arXiv
DO - 10.48550/arxiv.2611.02656
UR - https://arxiv.org/abs/2611.02656
AB - Non-Abelian black holes that violate the non-hair conjecture are known to exist in the Einstein-Yang-Mills-Higgs field theory. The onset of hair formation in this composed physical system is marked by the presence of `cloudy' black-hole spacetimes, magnetically charged Reissner-Nordström black holes that support spatially regular linearized field configurations. In the present paper we explore, using {\it analytical} techniques, the physical and mathematical properties of the composed black-hole-linearized-field bound-state configurations of the Einstein-Yang-Mills-Higgs theory. In particular, we derive a remarkably compact analytical formula for the discrete resonance spectrum {μ_k}^k=∞_k=1 of the dimensionless mass-radius parameter μ≡ m_w r_+ that characterizes the cloudy black-hole-field configurations in the regime 1≪ r_+≪ m^−1_w of small-mass weakly-magnetized black holes (here r_+ is the horizon radius of the central supporting black hole and m_w is the mass of the Yang-Mills field due to the Higgs effect). Interestingly, our results reveal that the excited black-hole-field resonances are characterized by the asymptotic k-independent dimensionless ratio μ_k+1/μ_k=e^−2π/√3.
ER -