Electroweak clouds supported by magnetically charged black holes: Analytic treatment along the existence-line
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866913671732527104 |
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| author | Hod, Shahar |
| author_facet | Hod, Shahar |
| contents | It has recently been revealed [R. Gervalle and M. S. Volkov, Phys. Rev. Lett. (2024)] that magnetically charged black holes of the composed Einstein-Weinberg-Salam field theory can support bound-state hairy configurations of electroweak fields. In the present paper we study, using {\it analytical} techniques, the physical and mathematical properties of the supported linearized electroweak fields (spatially regular electroweak 'clouds') in the dimensionless large-mass $μ\equiv m_{\text{w}} r_+\gg1$ regime of the composed black-hole-field system (here $m_{\text{w}}$ is the mass of the supported W-boson field and $r_+$ is the outer horizon radius of the central supporting black hole). In particular, we derive a remarkably compact formula for the discrete resonance spectrum $\{μ_k(n)\}_{k=0}^{k=\infty}$ that characterizes the composed black-hole-linearized-field configurations, where the integer $n\equiv 2Pe\in\mathbb{Z}$ characterizes the discrete charge parameter $P$ of the central magnetic Reissner-Nordström black hole and $e$ is the electron charge. The physical significance of the analytically derived resonant spectrum stems from the fact that, in the dimensionless large-charge $n\gg1$ regime, the fundamental (largest) eigenvalue $μ_0(n)$ determines the critical existence-line of the composed Einstein-Weinberg-Salam theory, a boundary line that separates hairy magnetic-black-hole-electroweak-field bound-state configurations from bald magnetic Reissner-Nordström black holes. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2501_18702 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Electroweak clouds supported by magnetically charged black holes: Analytic treatment along the existence-line Hod, Shahar General Relativity and Quantum Cosmology High Energy Astrophysical Phenomena High Energy Physics - Theory It has recently been revealed [R. Gervalle and M. S. Volkov, Phys. Rev. Lett. (2024)] that magnetically charged black holes of the composed Einstein-Weinberg-Salam field theory can support bound-state hairy configurations of electroweak fields. In the present paper we study, using {\it analytical} techniques, the physical and mathematical properties of the supported linearized electroweak fields (spatially regular electroweak 'clouds') in the dimensionless large-mass $μ\equiv m_{\text{w}} r_+\gg1$ regime of the composed black-hole-field system (here $m_{\text{w}}$ is the mass of the supported W-boson field and $r_+$ is the outer horizon radius of the central supporting black hole). In particular, we derive a remarkably compact formula for the discrete resonance spectrum $\{μ_k(n)\}_{k=0}^{k=\infty}$ that characterizes the composed black-hole-linearized-field configurations, where the integer $n\equiv 2Pe\in\mathbb{Z}$ characterizes the discrete charge parameter $P$ of the central magnetic Reissner-Nordström black hole and $e$ is the electron charge. The physical significance of the analytically derived resonant spectrum stems from the fact that, in the dimensionless large-charge $n\gg1$ regime, the fundamental (largest) eigenvalue $μ_0(n)$ determines the critical existence-line of the composed Einstein-Weinberg-Salam theory, a boundary line that separates hairy magnetic-black-hole-electroweak-field bound-state configurations from bald magnetic Reissner-Nordström black holes. |
| title | Electroweak clouds supported by magnetically charged black holes: Analytic treatment along the existence-line |
| topic | General Relativity and Quantum Cosmology High Energy Astrophysical Phenomena High Energy Physics - Theory |
| url | https://arxiv.org/abs/2501.18702 |