A note on integrated local energy decay estimates for spherically symmetric black hole spacetimes
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866916146329944064 |
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| author | Holzegel, Gustav Mavrogiannis, Georgios Ruiz, Renato Velozo |
| author_facet | Holzegel, Gustav Mavrogiannis, Georgios Ruiz, Renato Velozo |
| contents | We present short proofs of integrated local energy decay estimates on Schwarzschild, extremal Reissner-Nordström, and Schwarzschild-de Sitter spacetimes. The proofs employ novel global physical space multipliers, which, besides their remarkable simplicity, (a) are directly derivable from the geodesic flow, (b) do not require decomposition into spherical harmonics, and (c) whose boundary terms can be controlled by the conserved $T$-energy alone. We also elaborate on the intimate connection between the multipliers of the present paper and the globally good commutators introduced by the first two authors. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_02533 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A note on integrated local energy decay estimates for spherically symmetric black hole spacetimes Holzegel, Gustav Mavrogiannis, Georgios Ruiz, Renato Velozo General Relativity and Quantum Cosmology Analysis of PDEs We present short proofs of integrated local energy decay estimates on Schwarzschild, extremal Reissner-Nordström, and Schwarzschild-de Sitter spacetimes. The proofs employ novel global physical space multipliers, which, besides their remarkable simplicity, (a) are directly derivable from the geodesic flow, (b) do not require decomposition into spherical harmonics, and (c) whose boundary terms can be controlled by the conserved $T$-energy alone. We also elaborate on the intimate connection between the multipliers of the present paper and the globally good commutators introduced by the first two authors. |
| title | A note on integrated local energy decay estimates for spherically symmetric black hole spacetimes |
| topic | General Relativity and Quantum Cosmology Analysis of PDEs |
| url | https://arxiv.org/abs/2403.02533 |