Vacuum Petrov type D horizons of non-trivial $U(1)$ bundle structure over Riemann surfaces with genus $> 0$
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866914913182547968 |
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| author | Lewandowski, Jerzy Ossowski, Maciej |
| author_facet | Lewandowski, Jerzy Ossowski, Maciej |
| contents | We consider isolated horizons (Killing horizons up to the second order) whose null flow has the structure of a U(1) principal fiber bundle over a compact Riemann surface. We impose the vacuum Einstein equations (with the cosmological constant) and the condition that the spacetime Weyl tensor is of Petrov D type on the geometry of the horizons. We derive all the solutions in the case when the genus of the surface is $>1$. By doing so for all the non-trivial bundles, we complete the classification. We construct the embedding spacetimes and show that they are locally isometric to the toroidal or hyperbolic generalization of the Taub-NUT-(anti-) de Sitter spacetimes for horizons of genus $1$ or $>1$ respectively, after performing Misner's identification of the spacetime. The horizon bundle structure can be naturally extended to bundle structure defined on the entire spacetime. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_19383 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Vacuum Petrov type D horizons of non-trivial $U(1)$ bundle structure over Riemann surfaces with genus $> 0$ Lewandowski, Jerzy Ossowski, Maciej General Relativity and Quantum Cosmology We consider isolated horizons (Killing horizons up to the second order) whose null flow has the structure of a U(1) principal fiber bundle over a compact Riemann surface. We impose the vacuum Einstein equations (with the cosmological constant) and the condition that the spacetime Weyl tensor is of Petrov D type on the geometry of the horizons. We derive all the solutions in the case when the genus of the surface is $>1$. By doing so for all the non-trivial bundles, we complete the classification. We construct the embedding spacetimes and show that they are locally isometric to the toroidal or hyperbolic generalization of the Taub-NUT-(anti-) de Sitter spacetimes for horizons of genus $1$ or $>1$ respectively, after performing Misner's identification of the spacetime. The horizon bundle structure can be naturally extended to bundle structure defined on the entire spacetime. |
| title | Vacuum Petrov type D horizons of non-trivial $U(1)$ bundle structure over Riemann surfaces with genus $> 0$ |
| topic | General Relativity and Quantum Cosmology |
| url | https://arxiv.org/abs/2403.19383 |