From harmonic to Newman-Unti coordinates at the second post-Minkowskian order

TL;DR

This work constructs the complete transformation from harmonic to Newman–Unti coordinates for a generic metric up to second post-Minkowskian order ${\cal O}(G^2)$. By working with flat Bondi coordinates and expressing the harmonic metric in terms of NU coordinates, the authors derive the linear and quadratic transformation coefficients that map the perturbative metric into the NU gauge, enabling direct extraction of asymptotic data such as the Bondi shear, mass aspect, and angular-momentum aspect at each order. A key result is the explicit form of the NU metric components at ${\cal O}(G)$ and ${\cal O}(G^2)$, including logarithmic terms and the role of the order-$G$ supertranslation $\beta_1$ in the mass and angular-momentum sectors. The findings offer a concrete bridge between PM expansions and asymptotic radiation data, with potential impact on resolving discrepancies in angular-momentum loss in gravitational scattering and informing waveform template construction.

Abstract

In this paper, we present the complete transformations of a generic metric from harmonic to Newman-Unti coordinates up to the second post-Minkowskian order $(G^2)$. This allows us to determine the asymptotic shear, the Bondi mass aspect, and the angular-momentum aspect at both orders.