Renormalization of conformal infinity as a stretched horizon
Aldo Riello, Laurent Freidel
Abstract
Abstract In this paper, we provide a comprehensive study of asymptotically flat spacetime in even dimensions <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mi>d</mml:mi> <mml:mtext>⩾</mml:mtext> <mml:mn>4</mml:mn> </mml:mrow> </mml:math> . We analyze the most general boundary condition and asymptotic symmetry compatible with Penrose’s definition of asymptotic null infinity <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mrow> <mml:mrow> <mml:mi mathvariant="script">I</mml:mi> </mml:mrow> </mml:mrow> </mml:mrow> </mml:math> through conformal compactification. Following Penrose’s prescription and using a minimal version of the Bondi–Sachs gauge, we show that <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mrow> <mml:mrow> <mml:mi mathvariant="script">I</mml:mi> </mml:mrow> </mml:mrow> </mml:mrow> </mml:math> 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.