作为拉伸视界的共形无穷的重整化
Renormalization of conformal infinity as a stretched horizon
AI总结：
本文研究了偶数维渐近平直时空，通过共形紧致化将渐近类光无穷描述为拉伸视界，引入Carrollian应力张量，并为渐近辛势提供协变重整化方案以获得有限的辛通量和渐近荷。
摘要：
本文对偶数维 $d\geq 4$ 的渐近平直时空进行了全面研究。我们分析了与 Penrose 通过共形紧致化定义的渐近类光无穷 $\mathscr{I}$ 相容的最一般边界条件和渐近对称性。遵循 Penrose 的方案并使用 Bondi-Sachs 规范的最小版本，我们证明 $\mathscr{I}$ 自然配备了 Carrollian 应力张量，其径向导数定义了渐近 Weyl 张量。此分析将共形紧致化时空中的渐近无穷描述为拉伸视界。我们确立，荷荷方面的守恒可以写成渐近 Weyl 张量的 Carrollian Bianchi 恒等式。随后，我们为渐近辛势提供了协变重整化，从而得到有限的辛通量和渐近荷。该重整化方案即使在存在对数异常时也有效。
英文摘要：
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.
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