Asymptotic structure of the Pauli-Fierz theory in four spacetime dimensions

TL;DR

This paper analyzes the asymptotic structure of the Pauli-Fierz theory in four dimensions, revealing how improper gauge symmetries relate to BMS supertranslations and how the free theory's symmetries connect to full gravitational interactions.

Contribution

It identifies the boundary conditions invariant under improper gauge symmetries and demonstrates their relation to the BMS group in the context of the Pauli-Fierz theory.

Findings

Improper gauge symmetries correspond to BMS supertranslations.

Boundary conditions compatible with Lorentz invariance are established.

The free theory's asymptotic structure mirrors that of full gravity.

Abstract

The asymptotic structure of the Pauli-Fierz theory at spatial infinity is investigated in four spacetime dimensions. Boundary conditions on the massless spin-$2$ field that are invariant under an infinite-dimensional group of non-trivial ``improper'' gauge symmetries are given. The compatibility of these boundary conditions with invariance of the theory under Lorentz boosts is a subtle issue which is investigated in depth and leads to the identification of the improper gauge symmetries with the pure BMS supertranslations. It is also shown how rigid Poincar\'e transformations and improper gauge symmetries of the free Pauli-Fierz theory merge into the full BMS group as one switches on the gravitational coupling. Contrary to the massless spin-$1$ case, where invariance under boosts is implemented differently and where important differences between the free and the interacting cases have been exhibited recently, the free Pauli-Fierz theory and general relativity show very similar behaviours at spatial infinity.