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

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 Nöther 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 Nöther 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.

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