Renormalization of conformal infinity as a stretched horizon
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866914976586792960 |
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| author | Freidel, Laurent Riello, Aldo |
| author_facet | Freidel, Laurent Riello, Aldo |
| contents | In this paper, we provide a comprehensive study of asymptotically flat spacetime in even dimensions $d\geq 4$. We analyze the most general boundary condition and asymptotic symmetry compatible with Penrose's definition of asymptotic null infinity $\mathscr{I}$ through conformal compactification. Following Penrose's prescription and using a minimal version of the Bondi-Sachs gauge, we show that $\mathscr{I}$ is naturally equipped with a Carrollian stress tensor whose radial derivative defines the asymptotic Weyl tensor. This analysis describes asymptotic infinity as a stretched horizon in the conformally compactified spacetime. We establish that charge aspects conservation can be written as Carrollian Bianchi identities for the asymptotic Weyl tensor. We then provide a covariant renormalization for the asymptotic symplectic potential, which results in a finite symplectic flux and asymptotic charges. The renormalization scheme works even in the presence of logarithmic anomalies. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_03097 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Renormalization of conformal infinity as a stretched horizon Freidel, Laurent Riello, Aldo General Relativity and Quantum Cosmology High Energy Physics - Theory In this paper, we provide a comprehensive study of asymptotically flat spacetime in even dimensions $d\geq 4$. We analyze the most general boundary condition and asymptotic symmetry compatible with Penrose's definition of asymptotic null infinity $\mathscr{I}$ through conformal compactification. Following Penrose's prescription and using a minimal version of the Bondi-Sachs gauge, we show that $\mathscr{I}$ is naturally equipped with a Carrollian stress tensor whose radial derivative defines the asymptotic Weyl tensor. This analysis describes asymptotic infinity as a stretched horizon in the conformally compactified spacetime. We establish that charge aspects conservation can be written as Carrollian Bianchi identities for the asymptotic Weyl tensor. We then provide a covariant renormalization for the asymptotic symplectic potential, which results in a finite symplectic flux and asymptotic charges. The renormalization scheme works even in the presence of logarithmic anomalies. |
| title | Renormalization of conformal infinity as a stretched horizon |
| topic | General Relativity and Quantum Cosmology High Energy Physics - Theory |
| url | https://arxiv.org/abs/2402.03097 |