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 Poincaré 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 behaviors at spatial infinity.
Highlights
The study of the asymptotic properties of gravity in the asymptotically flat context is a remarkably rich subject that has undergone a revived interest in the last years [1]
We have worked out the asymptotic structure of the linearized Einstein theory
We have shown that it is described by the same infinite-dimensional symmetry group as the full interacting theory
Summary
The study of the asymptotic properties of gravity in the asymptotically flat context is a remarkably rich subject that has undergone a revived interest in the last years [1]. 37 (2020) 235011 asymptotic symmetries (analyzed either at null infinity [2,3,4,5,6,7,8] or at spatial infinity [9,10,11,12,13,14,15]) is infinite-dimensional and called the ‘BMS group’. The behavior of the Pauli–Fierz theory at null infinity was studied recently in [20], with a focus on different aspects of the theory It turns out—and we want to stress it from the outset—that Poincare invariance (more precisely, invariance under Lorentz boosts) plays a central role in the analysis. The discussion exhibits somewhat unanticipated differences between the free massless spin-1 and spin-2 fields
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