Probing the post-Minkowskian approximation using recursive addition of self-interactions

TL;DR

This paper demonstrates that the post-Minkowskian approximation can be derived from a recursive N"other coupling approach applied to the Pauli-Fierz spin-2 theory, establishing its independence from the weak-field limit of general relativity.

Contribution

It shows that the post-Minkowskian approximation is obtainable without weak-field assumptions, linking it to the recursive N"other coupling approach from flat spacetime spin-2 theory.

Findings

Post-Minkowskian approximation derived to third order from N"other coupling.

Establishes independence of post-Minkowskian from weak-field limit.

Connects linear spin-2 theory to gravitational wave analysis.

Abstract

We address the problem of deriving the post-Minkowskian approximation, widely used in current gravitational wave literature by investigating a possible deduction out of the recursive N\"other coupling approach, from the Pauli-Fierz spin-2 theory in flat spacetime. We find that this approach yields the post-Minkowskian approximation correctly to the first three orders, without invoking any weak-field limit of general relativity. This connection thus establishes that the post-Minkowskian approximation has a connotation independent of a weak-field expansion of general relativity, which is the manner usually presented in the literature. As a consequence, a link manifests between the recursive N\"other coupling approach to deriving general relativity from a linear spin-2 theory in flat spacetime and theoretical analyses of recent detection of gravitational wave events.