Celestial $w_{1+\infty}$ charges and the subleading structure of asymptotically-flat spacetimes

Geiller, Marc

doi:10.21468/SciPostPhys.18.1.023

SciPost Physics

Celestial $w_{1+\infty}$ charges and the subleading structure of asymptotically-flat spacetimes

Marc Geiller

SciPost Phys. 18, 023 (2025) · published 20 January 2025

doi: 10.21468/SciPostPhys.18.1.023
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Abstract

We study the subleading structure of asymptotically-flat spacetimes and its relationship to the $w_{1+∞}$ 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 $s$ brackets reproduce upon linearization the structure expected from the $w_{1+∞}$ 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 $w_{1+∞}$ algebra at linear order in the radiative data.

TY  - JOUR
PB  - SciPost Foundation
DO  - 10.21468/SciPostPhys.18.1.023
TI  - Celestial $w_{1+\infty}$ charges and the subleading structure of asymptotically-flat spacetimes
PY  - 2025/01/20
UR  - https://www.scipost.org/SciPostPhys.18.1.023
JF  - SciPost Physics
JA  - SciPost Phys.
VL  - 18
IS  - 1
SP  - 023
A1  - Geiller, Marc
AB  - We study the subleading structure of asymptotically-flat spacetimes and its relationship to the $w_{1+∞}$ 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 $s$ brackets reproduce upon linearization the structure expected from the $w_{1+∞}$ 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 $w_{1+∞}$ algebra at linear order in the radiative data.
ER  -

@Article{10.21468/SciPostPhys.18.1.023,
	title={{Celestial $w_{1+\infty}$ charges and the subleading structure of asymptotically-flat spacetimes}},
	author={Marc Geiller},
	journal={SciPost Phys.},
	volume={18},
	pages={023},
	year={2025},
	publisher={SciPost},
	doi={10.21468/SciPostPhys.18.1.023},
	url={https://scipost.org/10.21468/SciPostPhys.18.1.023},
}

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¹ ² ³ ⁴ Marc Geiller