Celestial w₁+ charges and the subleading structure of asymptotically-flat spacetimes

We study the subleading structure of asymptotically-flat spacetimes and its relationship to the w₁+∞ w1+∞ loop algebra of higher spin charges. We do so using both the Bondi–Sachs and the Newman–Penrose formalism, via a dictionary built from a preferred choice of tetrad. This enables us to access properties of the so-called higher Bondi aspects, such as their evolution equations, their transformation laws under asymptotic symmetries, and their relationship to the Newman–Penrose and the higher spin charges. By studying the recursive Einstein evolution equations defining these higher spin charges, we derive the general form of their transformation behavior under BMSW symmetries. This leads to an immediate proof that the spin 0, 1 and spin s s brackets reproduce upon linearization the structure expected from the w₁+∞ w1+∞ algebra. We then define renormalized higher spin charges which are conserved in the radiative vacuum at quadratic order, and show that they satisfy for all spins the w₁+∞ w1+∞ algebra at linear order in the radiative data.