The Asymptotic Structure of Gravity in Higher Even Dimensions

TL;DR

This paper explores the structure of asymptotic symmetries in higher even-dimensional gravity, specifically six dimensions, revealing non-linear features, defining radiative data, and establishing an infrared triangle linking charges, mass, and memory effects.

Contribution

It provides the first detailed analysis of asymptotic symmetries and charges in non-linear gravity beyond four dimensions, including a redefinition of radiative fields and boundary conditions.

Findings

Identified radiative data parametrized by symmetric trace-free tensors.

Derived super-translation charges consistent with equations of motion.

Established the connection between super-translation charge, Bondi mass, and gravitational memory.

Abstract

We investigate the notion of asymptotic symmetries in classical gravity in higher even dimensions, with $D = 6$ space-time dimensions as the prototype. Unlike in four dimensions, certain non-linearities persist which necessitates the complete non-linear analysis we undertake. We show that the free data is parametrized by a pair of symmetric trace-free tensors at future (past) null infinity. This involves a redefinition of the radiative field. We define a symplectic structure generating the radiative phase space at ${\cal I}^{\pm}$ with appropriate boundary conditions which are preserved by the action of supertranslations. We derive the charge associated to super-translation vector fields and this charge matches with that derived using the equations of motion in the full non-linear theory. We elaborate on the precise relationship between the super-translation charge, the Bondi mass aspect and the "gravitational memory" in six space-time dimensions, thus providing the first example of an infrared triangle in non-linear gravity beyond four dimensions.