Symmetries of extremal horizons
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866908704913227776 |
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| author | Colling, Alex |
| author_facet | Colling, Alex |
| contents | We prove an intrinsic analogue of Hawking's rigidity theorem for extremal horizons in arbitrary dimensions: any compact cross-section of a rotating extremal horizon in a spacetime satisfying the null energy condition must admit a Killing vector field. If the dominant energy condition is satisfied for null vectors, it follows that an extension of the near-horizon geometry admits an enhanced isometry group containing $SO(2,1)$ or the 2D Poincaré group $\mathbb{R}^2 \rtimes SO(1,1)$. In the latter case, the associated Aretakis instability for a massless scalar field is shifted by one order in the derivatives of the field transverse to the horizon. We consider a broad class of examples including Einstein-Maxwell(-Chern-Simons) theory and Yang-Mills theory coupled to charged matter. In these examples we show that the symmetries are inherited by the matter fields. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2512_10200 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Symmetries of extremal horizons Colling, Alex General Relativity and Quantum Cosmology High Energy Physics - Theory Differential Geometry We prove an intrinsic analogue of Hawking's rigidity theorem for extremal horizons in arbitrary dimensions: any compact cross-section of a rotating extremal horizon in a spacetime satisfying the null energy condition must admit a Killing vector field. If the dominant energy condition is satisfied for null vectors, it follows that an extension of the near-horizon geometry admits an enhanced isometry group containing $SO(2,1)$ or the 2D Poincaré group $\mathbb{R}^2 \rtimes SO(1,1)$. In the latter case, the associated Aretakis instability for a massless scalar field is shifted by one order in the derivatives of the field transverse to the horizon. We consider a broad class of examples including Einstein-Maxwell(-Chern-Simons) theory and Yang-Mills theory coupled to charged matter. In these examples we show that the symmetries are inherited by the matter fields. |
| title | Symmetries of extremal horizons |
| topic | General Relativity and Quantum Cosmology High Energy Physics - Theory Differential Geometry |
| url | https://arxiv.org/abs/2512.10200 |