Black holes with electroweak hair -- the detailed derivation
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866915326630821888 |
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| author | Gervalle, Romain Volkov, Mikhail S. |
| author_facet | Gervalle, Romain Volkov, Mikhail S. |
| contents | We present a very detailed derivation of solutions describing hairy black holes within the gravity-coupled Weinberg-Salam theory, which were previously reported in \href{https://doi.org/10.1103/PhysRevLett.133.171402}{Phys.Rev.Lett. 133 (2024) 171402}. These black holes support a strong magnetic field that polarizes the electroweak vacuum and creates a condensate of massive fields carrying superconducting currents along the black hole horizon. The currents, in turn, generate a ``corona'' of magnetic vortex segments attached to the horizon at both ends. The condensate and corona together constitute the black hole hair. The extremal solutions approach, in the far field, the magnetic Reissner-Nordström configuration, with a total mass that is {\it lower} than the total charge, $M<|Q|$, due to the negative Zeeman energy of the condensate. This makes the removal of the hair energetically unfavorable. The maximally hairy black holes exhibit masses comparable to terrestrial values, with approximately 11\% of their total mass stored in the hair. Given that these solutions arise within a well-tested theoretical framework, they are likely to have physical relevance. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2504_09304 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Black holes with electroweak hair -- the detailed derivation Gervalle, Romain Volkov, Mikhail S. High Energy Physics - Theory High Energy Astrophysical Phenomena General Relativity and Quantum Cosmology High Energy Physics - Phenomenology We present a very detailed derivation of solutions describing hairy black holes within the gravity-coupled Weinberg-Salam theory, which were previously reported in \href{https://doi.org/10.1103/PhysRevLett.133.171402}{Phys.Rev.Lett. 133 (2024) 171402}. These black holes support a strong magnetic field that polarizes the electroweak vacuum and creates a condensate of massive fields carrying superconducting currents along the black hole horizon. The currents, in turn, generate a ``corona'' of magnetic vortex segments attached to the horizon at both ends. The condensate and corona together constitute the black hole hair. The extremal solutions approach, in the far field, the magnetic Reissner-Nordström configuration, with a total mass that is {\it lower} than the total charge, $M<|Q|$, due to the negative Zeeman energy of the condensate. This makes the removal of the hair energetically unfavorable. The maximally hairy black holes exhibit masses comparable to terrestrial values, with approximately 11\% of their total mass stored in the hair. Given that these solutions arise within a well-tested theoretical framework, they are likely to have physical relevance. |
| title | Black holes with electroweak hair -- the detailed derivation |
| topic | High Energy Physics - Theory High Energy Astrophysical Phenomena General Relativity and Quantum Cosmology High Energy Physics - Phenomenology |
| url | https://arxiv.org/abs/2504.09304 |