Peeling for tensorial wave equations on Schwarzschild spacetime
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2022
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| _version_ | 1866908880446947328 |
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| author | Xuan, Pham Truong |
| author_facet | Xuan, Pham Truong |
| contents | In this paper, we establish the asymptotic behaviour along outgoing and incoming radial geodesics, i.e., the peeling property for the tensorial Fackrell-Ipser and spin $\pm 1$ Teukolsky equations on Schwarzschild spacetime. Our method combines a conformal compactification with vector field techniques to prove the two-side estimates of the energies of tensorial fields through the future and past null infinity $\mathscr{I}^\pm$ and the initial Cauchy hypersurface $Σ_0 = \left\{ t=0 \right\}$ in a neighbourhood of spacelike infinity $i_0$ far away from the horizon and future timelike infinity. Our results obtain the optimal initial data which guarantees the peeling at all orders. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2206_02193 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Peeling for tensorial wave equations on Schwarzschild spacetime Xuan, Pham Truong General Relativity and Quantum Cosmology Mathematical Physics Analysis of PDEs Differential Geometry In this paper, we establish the asymptotic behaviour along outgoing and incoming radial geodesics, i.e., the peeling property for the tensorial Fackrell-Ipser and spin $\pm 1$ Teukolsky equations on Schwarzschild spacetime. Our method combines a conformal compactification with vector field techniques to prove the two-side estimates of the energies of tensorial fields through the future and past null infinity $\mathscr{I}^\pm$ and the initial Cauchy hypersurface $Σ_0 = \left\{ t=0 \right\}$ in a neighbourhood of spacelike infinity $i_0$ far away from the horizon and future timelike infinity. Our results obtain the optimal initial data which guarantees the peeling at all orders. |
| title | Peeling for tensorial wave equations on Schwarzschild spacetime |
| topic | General Relativity and Quantum Cosmology Mathematical Physics Analysis of PDEs Differential Geometry |
| url | https://arxiv.org/abs/2206.02193 |