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| Format: | Preprint |
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2025
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| Online Access: | https://arxiv.org/abs/2507.13306 |
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| _version_ | 1866914326846111744 |
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| author | Lu, Zhenkang Ran, Cheng Wu, Shao-feng |
| author_facet | Lu, Zhenkang Ran, Cheng Wu, Shao-feng |
| contents | The holographic Green's function becomes ambiguous, taking the indeterminate form `$0/0$', at an infinite set of special frequencies and momenta known as ``pole-skipping points''. In this work, we propose that these pole-skipping points can be used to reconstruct both the interior and exterior geometry of a static, planar-symmetric black hole in the bulk. The entire reconstruction procedure is fully analytical and only involves solving a system of linear equations. We demonstrate its effectiveness across various backgrounds, including the BTZ black hole, its $T\bar{T}$-deformed counterparts, as well as geometries with Lifshitz scaling and hyperscaling-violation. Within this framework, other geometric quantities, such as the vacuum Einstein equations, can also be reinterpreted directly in terms of pole-skipping data. Moreover, our approach reveals a hidden algebraic structure governing the pole-skipping points of Klein-Gordon equations of the form $(\nabla^{2} + V(r))ϕ(r) = 0$: only a subset of these points is independent, while the remainder is constrained by an equal number of homogeneous polynomial identities in the pole-skipping momenta. These identities are universal, as confirmed by their validity across a broad class of bulk geometries with varying dimensionality, boundary asymptotics, and perturbation modes. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_13306 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The Algebraic Structure Underlying Pole-Skipping Points Lu, Zhenkang Ran, Cheng Wu, Shao-feng High Energy Physics - Theory The holographic Green's function becomes ambiguous, taking the indeterminate form `$0/0$', at an infinite set of special frequencies and momenta known as ``pole-skipping points''. In this work, we propose that these pole-skipping points can be used to reconstruct both the interior and exterior geometry of a static, planar-symmetric black hole in the bulk. The entire reconstruction procedure is fully analytical and only involves solving a system of linear equations. We demonstrate its effectiveness across various backgrounds, including the BTZ black hole, its $T\bar{T}$-deformed counterparts, as well as geometries with Lifshitz scaling and hyperscaling-violation. Within this framework, other geometric quantities, such as the vacuum Einstein equations, can also be reinterpreted directly in terms of pole-skipping data. Moreover, our approach reveals a hidden algebraic structure governing the pole-skipping points of Klein-Gordon equations of the form $(\nabla^{2} + V(r))ϕ(r) = 0$: only a subset of these points is independent, while the remainder is constrained by an equal number of homogeneous polynomial identities in the pole-skipping momenta. These identities are universal, as confirmed by their validity across a broad class of bulk geometries with varying dimensionality, boundary asymptotics, and perturbation modes. |
| title | The Algebraic Structure Underlying Pole-Skipping Points |
| topic | High Energy Physics - Theory |
| url | https://arxiv.org/abs/2507.13306 |