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| Format: | Preprint |
| Published: |
2026
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| Online Access: | https://arxiv.org/abs/2604.02084 |
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| _version_ | 1866911728084713472 |
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| author | Tullini, Alex |
| author_facet | Tullini, Alex |
| contents | We study the conformal wave equation $\square_g ψ+ \frac{2}{l^2} ψ= 0$ on 4-dimensional Schwarzschild--Anti de Sitter spacetimes under dissipative boundary conditions. We prove boundedness and decay of the non-degenerate energy of $ψ$ at an arbitrary polynomial rate of $(1+v)^{-n}$ provided that we control the (up to) $n$-times $T$-commuted energy. This contrasts with the inverse logarithmic decay obtained under Dirichlet boundary conditions and is in line with the result obtained in the pure Anti-de Sitter case under dissipative boundary conditions. In particular, the decay is not affected by the additional trapping at the photon sphere. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_02084 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Boundedness and decay for the conformal wave equation in Schwarzschild-AdS under dissipative boundary conditions Tullini, Alex General Relativity and Quantum Cosmology Analysis of PDEs We study the conformal wave equation $\square_g ψ+ \frac{2}{l^2} ψ= 0$ on 4-dimensional Schwarzschild--Anti de Sitter spacetimes under dissipative boundary conditions. We prove boundedness and decay of the non-degenerate energy of $ψ$ at an arbitrary polynomial rate of $(1+v)^{-n}$ provided that we control the (up to) $n$-times $T$-commuted energy. This contrasts with the inverse logarithmic decay obtained under Dirichlet boundary conditions and is in line with the result obtained in the pure Anti-de Sitter case under dissipative boundary conditions. In particular, the decay is not affected by the additional trapping at the photon sphere. |
| title | Boundedness and decay for the conformal wave equation in Schwarzschild-AdS under dissipative boundary conditions |
| topic | General Relativity and Quantum Cosmology Analysis of PDEs |
| url | https://arxiv.org/abs/2604.02084 |