Renormalization of conformal infinity as a stretched horizon

TL;DR

This work develops a comprehensive framework for asymptotically flat spacetimes in even dimensions using Penrose conformal infinity and Bondi–Sachs gauge. It recasts null infinity as a stretched Carrollian horizon, identifying a Carrollian stress tensor whose radial evolution encodes the asymptotic Weyl tensor and charge aspects via Bianchi identities. A covariant, two-step renormalization of the symplectic potential yields finite fluxes and charges even in the presence of logarithmic anomalies, providing a robust foundation for higher-dimensional BMS-like symmetries and their relation to gravitational radiation. The results connect the conformal-frame dynamics (Weyl, Schouten, and conformal stress tensor) with the radiative data and the Carrollian fluid interpretation, offering a unified perspective on asymptotic symmetries, charge conservation, and holographic renormalization of gravity.

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.