Shielding linearized gravity

Abstract

We present an elementary argument that one can shield linearised gravitational fields using linearised gravitational fields. This is done by using third-order potentials for the metric, which avoids the need to solve singular equations in shielding or gluing constructions for the linearised metric.

Same Diff? Part II: A compendium of similarities between gauge transformations and diffeomorphisms

“…23 See Beig & Chruściel (2017); Carlotto & Schoen (2016) for some interesting shielding results in perturbative and non-perturbative gravity, respectively.…”

On linearised vacuum constraint equations on Einstein manifolds*

“…Recall that in [3] (compare [8]) we provided a simple way of shielding gravity linearised at Minkowski space in transverse-traceless gauge (in a sense made precise by Theorem 1.1 below), based on third-order unconstrained potentials for transverse-traceless tensors introduced in [2]. One of the motivations for the current work was to provide a shielding construction for linearised vacuum gravity which applies to initial data with a non-zero cosmological constant Λ, regardless of its sign and of the gauge.…”

“…In the screening construction of [3] one needs first to transform the metric to a transverse-traceless gauge, which requires solving elliptic equations. Neither solving elliptic equations, nor applying preliminary gauge transformations, is needed in the approach taken here.…”

“…As discussed in [3], a shielding construction provides immediately a gluing construction, the reader is referred to [3] for details.…”

“…The proof of Theorem 1.1 is a repetition of the arguments given in [3,Section 2.3], invoking instead the potentials of Theorems 3.1 and 3.2, and will be omitted.…”