Celestial $w_{1+\infty}$ charges and the subleading structure of asymptotically-flat spacetimes
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 pro...
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2025-01-01
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| author | Marc Geiller |
| author_facet | Marc Geiller |
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| description | 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. |
| format | Article |
| id | doaj-art-29053308134449bc9a3ff761df82c887 |
| institution | Kabale University |
| issn | 2542-4653 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | SciPost |
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| series | SciPost Physics |
| spelling | doaj-art-29053308134449bc9a3ff761df82c8872025-01-20T13:59:51ZengSciPostSciPost Physics2542-46532025-01-0118102310.21468/SciPostPhys.18.1.023Celestial $w_{1+\infty}$ charges and the subleading structure of asymptotically-flat spacetimesMarc GeillerWe 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.https://scipost.org/SciPostPhys.18.1.023 |
| spellingShingle | Marc Geiller Celestial $w_{1+\infty}$ charges and the subleading structure of asymptotically-flat spacetimes SciPost Physics |
| title | Celestial $w_{1+\infty}$ charges and the subleading structure of asymptotically-flat spacetimes |
| title_full | Celestial $w_{1+\infty}$ charges and the subleading structure of asymptotically-flat spacetimes |
| title_fullStr | Celestial $w_{1+\infty}$ charges and the subleading structure of asymptotically-flat spacetimes |
| title_full_unstemmed | Celestial $w_{1+\infty}$ charges and the subleading structure of asymptotically-flat spacetimes |
| title_short | Celestial $w_{1+\infty}$ charges and the subleading structure of asymptotically-flat spacetimes |
| title_sort | celestial w 1 infty charges and the subleading structure of asymptotically flat spacetimes |
| url | https://scipost.org/SciPostPhys.18.1.023 |
| work_keys_str_mv | AT marcgeiller celestialw1inftychargesandthesubleadingstructureofasymptoticallyflatspacetimes |