Gravitational Observatories in AdS$_4$
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866911103128174592 |
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| author | Anninos, Dionysios Arias, Raúl Galante, Damián A. Maneerat, Chawakorn |
| author_facet | Anninos, Dionysios Arias, Raúl Galante, Damián A. Maneerat, Chawakorn |
| contents | We consider four-dimensional general relativity with a negative cosmological constant in the presence of a finite size boundary, $Γ$, for both Euclidean and Lorentzian signature. As our boundary condition, we consider the `conformal' boundary condition that fixes the conformal class of the induced metric at $Γ$ and the trace of the extrinsic curvature, $K(x^m)$. In Lorentzian signature, we must supplement these with appropriate initial data comprising the standard Cauchy data along a spatial slice and, in addition, initial data for a boundary mode that appears due to the presence of the finite size boundary. We perform a linearised analysis of the gravitational field equations for both an $S^2\times \mathbb{R}$ as well as a Minkowskian, $\mathbb{R}^{1,2}$, boundary. In the $S^2\times \mathbb{R}$ case, in addition to the usual AdS$_4$ normal modes, we uncover a novel linearised perturbation, $\boldsymbolω(x^m)$, which can exhibit complex frequencies at sufficiently large angular momentum. Upon moving $Γ$ toward the infinite asymptotic AdS$_4$ boundary, the complex frequencies appear at increasingly large angular momentum and vanish altogether in the strict limit. In the $\mathbb{R}^{2,1}$ case, although we uncover an analogous novel perturbation, we show it does not exhibit complex frequencies. In Euclidean signature, we show that $K(x^m)$ plays the role of a source for $\boldsymbolω(x^m)$. When close to the AdS$_4$ asymptotic boundary, we speculate on the holographic interpretation of $\boldsymbolω(x^m)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_16305 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Gravitational Observatories in AdS$_4$ Anninos, Dionysios Arias, Raúl Galante, Damián A. Maneerat, Chawakorn High Energy Physics - Theory General Relativity and Quantum Cosmology We consider four-dimensional general relativity with a negative cosmological constant in the presence of a finite size boundary, $Γ$, for both Euclidean and Lorentzian signature. As our boundary condition, we consider the `conformal' boundary condition that fixes the conformal class of the induced metric at $Γ$ and the trace of the extrinsic curvature, $K(x^m)$. In Lorentzian signature, we must supplement these with appropriate initial data comprising the standard Cauchy data along a spatial slice and, in addition, initial data for a boundary mode that appears due to the presence of the finite size boundary. We perform a linearised analysis of the gravitational field equations for both an $S^2\times \mathbb{R}$ as well as a Minkowskian, $\mathbb{R}^{1,2}$, boundary. In the $S^2\times \mathbb{R}$ case, in addition to the usual AdS$_4$ normal modes, we uncover a novel linearised perturbation, $\boldsymbolω(x^m)$, which can exhibit complex frequencies at sufficiently large angular momentum. Upon moving $Γ$ toward the infinite asymptotic AdS$_4$ boundary, the complex frequencies appear at increasingly large angular momentum and vanish altogether in the strict limit. In the $\mathbb{R}^{2,1}$ case, although we uncover an analogous novel perturbation, we show it does not exhibit complex frequencies. In Euclidean signature, we show that $K(x^m)$ plays the role of a source for $\boldsymbolω(x^m)$. When close to the AdS$_4$ asymptotic boundary, we speculate on the holographic interpretation of $\boldsymbolω(x^m)$. |
| title | Gravitational Observatories in AdS$_4$ |
| topic | High Energy Physics - Theory General Relativity and Quantum Cosmology |
| url | https://arxiv.org/abs/2412.16305 |