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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2512.03587 |
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| _version_ | 1866917340001599488 |
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| author | Enciso, Alberto Uhlmann, Gunther Wrochna, Michał |
| author_facet | Enciso, Alberto Uhlmann, Gunther Wrochna, Michał |
| contents | We consider the Klein-Gordon equation on asymptotically anti-de Sitter spacetimes, and show that the forward Dirichlet-to-Neumann map (or scattering matrix) is a fractional power of the boundary wave operator modulo lower order terms in the sense of paired Lagrangian distributions. We use it to show that, outside of a countable set of mass parameters, the Dirichlet-to-Neumann map determines the Taylor series of the bulk metric at the boundary, and hence allows the recovery of a real analytic metric or Einstein metric modulo isometries. Furthermore, we prove a Lorentzian version of the Graham-Zworski theorem relating poles of the Dirichlet-to-Neumann map to conformally invariant powers of the boundary wave operator. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_03587 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The Dirichlet-to-Neumann map on asymptotically anti-de Sitter spaces and holography Enciso, Alberto Uhlmann, Gunther Wrochna, Michał Analysis of PDEs Mathematical Physics Differential Geometry We consider the Klein-Gordon equation on asymptotically anti-de Sitter spacetimes, and show that the forward Dirichlet-to-Neumann map (or scattering matrix) is a fractional power of the boundary wave operator modulo lower order terms in the sense of paired Lagrangian distributions. We use it to show that, outside of a countable set of mass parameters, the Dirichlet-to-Neumann map determines the Taylor series of the bulk metric at the boundary, and hence allows the recovery of a real analytic metric or Einstein metric modulo isometries. Furthermore, we prove a Lorentzian version of the Graham-Zworski theorem relating poles of the Dirichlet-to-Neumann map to conformally invariant powers of the boundary wave operator. |
| title | The Dirichlet-to-Neumann map on asymptotically anti-de Sitter spaces and holography |
| topic | Analysis of PDEs Mathematical Physics Differential Geometry |
| url | https://arxiv.org/abs/2512.03587 |