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| Format: | Preprint |
| Veröffentlicht: |
2024
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| Online-Zugang: | https://arxiv.org/abs/2411.12568 |
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| _version_ | 1866916487952859136 |
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| author | Hintz, Peter |
| author_facet | Hintz, Peter |
| contents | On a class of dynamical spacetimes which are asymptotic as $t\to\infty$ to a stationary spacetime containing a horizon $\mathcal{H}_0$, we show the existence of a unique null hypersurface $\mathcal{H}$ which is asymptotic to $\mathcal{H}_0$. This is a special case of a general unstable manifold theorem for perturbations of flows which translate in time and have a normal sink at an invariant manifold in space. Examples of horizons $\mathcal{H}_0$ to which our result applies include event horizons of subextremal Kerr and Kerr-Newman black holes as well as event and cosmological horizons of subextremal Kerr-Newman-de Sitter black holes. In the Kerr(-Newman) case, we show that $\mathcal{H}$ is equal to the boundary of the black hole region of the dynamical spacetime. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_12568 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Horizons of some asymptotically stationary spacetimes Hintz, Peter General Relativity and Quantum Cosmology Differential Geometry Dynamical Systems Primary: 37C70, Secondary: 83C57, 53B50 On a class of dynamical spacetimes which are asymptotic as $t\to\infty$ to a stationary spacetime containing a horizon $\mathcal{H}_0$, we show the existence of a unique null hypersurface $\mathcal{H}$ which is asymptotic to $\mathcal{H}_0$. This is a special case of a general unstable manifold theorem for perturbations of flows which translate in time and have a normal sink at an invariant manifold in space. Examples of horizons $\mathcal{H}_0$ to which our result applies include event horizons of subextremal Kerr and Kerr-Newman black holes as well as event and cosmological horizons of subextremal Kerr-Newman-de Sitter black holes. In the Kerr(-Newman) case, we show that $\mathcal{H}$ is equal to the boundary of the black hole region of the dynamical spacetime. |
| title | Horizons of some asymptotically stationary spacetimes |
| topic | General Relativity and Quantum Cosmology Differential Geometry Dynamical Systems Primary: 37C70, Secondary: 83C57, 53B50 |
| url | https://arxiv.org/abs/2411.12568 |