Renormalization of conformal infinity as a stretched horizon

Abstract

In this paper, we provide a comprehensive study of asymptotically flat spacetime in even dimensions $d\ge 4$. We analyze the most general boundary condition and asymptotic symmetry compatible with Penrose's definition of asymptotic null infinity $\mathcal{I}$ through conformal compactification. Following Penrose's prescription and using a minimal version of the Bondi-Sachs gauge, we show that $\mathcal{I}$ 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.

v3: published version; a few updates wrt v2 based on referees' feedback. v2: submitted version; major updates wrt v1 (see that version for details)