Late-time tails for linear waves on radially symmetric stationary spacetimes of two space dimensions
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arXiv
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866909037376831488 |
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| author | Gautam, Onyx |
| author_facet | Gautam, Onyx |
| contents | We show that the leading-order term in the late-time asymptotics of solutions to the linear wave equation on radially symmetric stationary perturbations of $(2 + 1)$-dimensional Minkowski space is proportional to $u^{-1/2}v^{-1/2}$ (which solves the wave equation on Minkowski space), where $u$ and $v$ are double null coordinates. Our proof adapts the physical space techniques in the work of Gajic (arXiv:2203.15838) on the wave equation with an inverse-square potential on the Schwarzschild spacetime. In particular, we extend the $r^p$-weighted energy estimates of Dafermos--Rodnianski (arXiv:0910.4957) to two space dimensions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_03220 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Late-time tails for linear waves on radially symmetric stationary spacetimes of two space dimensions Gautam, Onyx Analysis of PDEs General Relativity and Quantum Cosmology We show that the leading-order term in the late-time asymptotics of solutions to the linear wave equation on radially symmetric stationary perturbations of $(2 + 1)$-dimensional Minkowski space is proportional to $u^{-1/2}v^{-1/2}$ (which solves the wave equation on Minkowski space), where $u$ and $v$ are double null coordinates. Our proof adapts the physical space techniques in the work of Gajic (arXiv:2203.15838) on the wave equation with an inverse-square potential on the Schwarzschild spacetime. In particular, we extend the $r^p$-weighted energy estimates of Dafermos--Rodnianski (arXiv:0910.4957) to two space dimensions. |
| title | Late-time tails for linear waves on radially symmetric stationary spacetimes of two space dimensions |
| topic | Analysis of PDEs General Relativity and Quantum Cosmology |
| url | https://arxiv.org/abs/2605.03220 |