Renormalization of conformal infinity as a stretched horizon

TL;DR

This paper studies the structure of asymptotically flat spacetimes in even dimensions, revealing how conformal infinity can be viewed as a stretched horizon and establishing a renormalization scheme for asymptotic charges.

Contribution

It introduces a covariant renormalization of the symplectic potential and describes conformal infinity as a stretched horizon with a Carrollian stress tensor.

Findings

Conformal infinity is described as a stretched horizon.

A Carrollian stress tensor is naturally defined at infinity.

A finite symplectic flux and charges are achieved through renormalization.

Abstract

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.