Stability for linearized gravity on the Kerr spacetime
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arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2019
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| _version_ | 1866915244228476928 |
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| author | Andersson, Lars Bäckdahl, Thomas Blue, Pieter Ma, Siyuan |
| author_facet | Andersson, Lars Bäckdahl, Thomas Blue, Pieter Ma, Siyuan |
| contents | In this paper we prove integrated energy and pointwise decay estimates for solutions of the vacuum linearized Einstein equation on the domain of outer communication of the Kerr black hole spacetime. The estimates are valid for the full subextreme range of Kerr black holes, provided integrated energy estimates for the Teukolsky equation hold. For slowly rotating Kerr backgrounds, such estimates are known to hold, due to the work of one of the authors. The results in this paper thus provide the first stability results for linearized gravity on the Kerr background, in the slowly rotating case, and reduce the linearized stability problem for the full subextreme range to proving integrated energy estimates for the Teukolsky equation. This constitutes an essential step towards a proof of the black hole stability conjecture, i.e. the statement that the Kerr family is dynamically stable, one of the central open problems in general relativity. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1903_03859 |
| institution | arXiv |
| publishDate | 2019 |
| record_format | arxiv |
| spellingShingle | Stability for linearized gravity on the Kerr spacetime Andersson, Lars Bäckdahl, Thomas Blue, Pieter Ma, Siyuan Analysis of PDEs General Relativity and Quantum Cosmology 35F40, 35L15, 35Q76, 83C35, 83C57, 83C60 In this paper we prove integrated energy and pointwise decay estimates for solutions of the vacuum linearized Einstein equation on the domain of outer communication of the Kerr black hole spacetime. The estimates are valid for the full subextreme range of Kerr black holes, provided integrated energy estimates for the Teukolsky equation hold. For slowly rotating Kerr backgrounds, such estimates are known to hold, due to the work of one of the authors. The results in this paper thus provide the first stability results for linearized gravity on the Kerr background, in the slowly rotating case, and reduce the linearized stability problem for the full subextreme range to proving integrated energy estimates for the Teukolsky equation. This constitutes an essential step towards a proof of the black hole stability conjecture, i.e. the statement that the Kerr family is dynamically stable, one of the central open problems in general relativity. |
| title | Stability for linearized gravity on the Kerr spacetime |
| topic | Analysis of PDEs General Relativity and Quantum Cosmology 35F40, 35L15, 35Q76, 83C35, 83C57, 83C60 |
| url | https://arxiv.org/abs/1903.03859 |