General Effective Theories of Black Holes in the Large D Limit
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| author | Emparan, Roberto Rafecas-Ventosa, Jordi Way, Benson |
| author_facet | Emparan, Roberto Rafecas-Ventosa, Jordi Way, Benson |
| contents | We derive the general form of the effective equations governing black hole dynamics in the limit of a large number of dimensions $D$. These split into a universal \emph{soap-bubble} embedding condition for stationary configurations and a set of nonlinear dynamical evolution equations describing near-horizon fluctuations of $O(1/D)$ amplitude over horizon scales of $O(1/\sqrt{D})$. We obtain these equations in full generality, including arbitrary asymptotic sources in the near-horizon region, and we show that they form a parabolic system with a well-posed initial value problem. To connect the various approaches to large-$D$ black hole dynamics, we also show that both the embedding and dynamical equations can be derived from the covariant membrane formalism. We clarify the intrinsic scope of the large-$D$ approach, emphasizing that it yields a well-posed dynamical evolution only on horizon scales of $O(1/\sqrt{D})$, which is the range where the most relevant horizon dynamics occur. Our results highlight the versatility of these effective theories for studying a wide class of black hole phenomena. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_14186 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | General Effective Theories of Black Holes in the Large D Limit Emparan, Roberto Rafecas-Ventosa, Jordi Way, Benson High Energy Physics - Theory General Relativity and Quantum Cosmology We derive the general form of the effective equations governing black hole dynamics in the limit of a large number of dimensions $D$. These split into a universal \emph{soap-bubble} embedding condition for stationary configurations and a set of nonlinear dynamical evolution equations describing near-horizon fluctuations of $O(1/D)$ amplitude over horizon scales of $O(1/\sqrt{D})$. We obtain these equations in full generality, including arbitrary asymptotic sources in the near-horizon region, and we show that they form a parabolic system with a well-posed initial value problem. To connect the various approaches to large-$D$ black hole dynamics, we also show that both the embedding and dynamical equations can be derived from the covariant membrane formalism. We clarify the intrinsic scope of the large-$D$ approach, emphasizing that it yields a well-posed dynamical evolution only on horizon scales of $O(1/\sqrt{D})$, which is the range where the most relevant horizon dynamics occur. Our results highlight the versatility of these effective theories for studying a wide class of black hole phenomena. |
| title | General Effective Theories of Black Holes in the Large D Limit |
| topic | High Energy Physics - Theory General Relativity and Quantum Cosmology |
| url | https://arxiv.org/abs/2512.14186 |