Dynamical Horizon Segments and Spacetime Isometries
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866918146890268672 |
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| author | Ashtekar, Abhay Krishnan, Badri |
| author_facet | Ashtekar, Abhay Krishnan, Badri |
| contents | Given a space-time $(\mathscr{M}, g_{ab})$ admitting a dynamical horizon segment (DHS) $\mathscr{H}$, we show that there are stringent constraints on the Killing fields $ξ^a$ that $g_{ab}$ can admit in a neighborhood of $\mathscr{H}$: Generically, $ξ^a$ can only be a rotational Killing field which, furthermore, leaves each marginally trapped 2-sphere cross-section $\mathcal{S}$ of $\mathscr{H}$ invariant. Finally, if $ξ^a$ happens to be hypersurface orthogonal near $\mathscr{H}$, then, not only the angular momentum but also all spin multipoles vanish on every $\mathcal{S}$; the entire spin structure of these DHSs is indistinguishable from that of spherically symmetric DHSs! |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_10190 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Dynamical Horizon Segments and Spacetime Isometries Ashtekar, Abhay Krishnan, Badri General Relativity and Quantum Cosmology High Energy Physics - Theory Mathematical Physics Given a space-time $(\mathscr{M}, g_{ab})$ admitting a dynamical horizon segment (DHS) $\mathscr{H}$, we show that there are stringent constraints on the Killing fields $ξ^a$ that $g_{ab}$ can admit in a neighborhood of $\mathscr{H}$: Generically, $ξ^a$ can only be a rotational Killing field which, furthermore, leaves each marginally trapped 2-sphere cross-section $\mathcal{S}$ of $\mathscr{H}$ invariant. Finally, if $ξ^a$ happens to be hypersurface orthogonal near $\mathscr{H}$, then, not only the angular momentum but also all spin multipoles vanish on every $\mathcal{S}$; the entire spin structure of these DHSs is indistinguishable from that of spherically symmetric DHSs! |
| title | Dynamical Horizon Segments and Spacetime Isometries |
| topic | General Relativity and Quantum Cosmology High Energy Physics - Theory Mathematical Physics |
| url | https://arxiv.org/abs/2506.10190 |