Unified Treatment of null and Spatial Infinity IV: Angular Momentum at Null and Spatial Infinity
| Autor: | Ashtekar, Abhay, Khera, Neev |
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| Rok vydání: | 2023 |
| Předmět: | |
| Zdroj: | JHEP01 (2024) 085 |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1007/JHEP01(2024)085 |
| Popis: | In a companion paper we introduced the notion of asymptotically Minkowski spacetimes. These space-times are asymptotically flat at both null and spatial infinity, and furthermore there is a harmonious matching of limits of certain fields as one approaches $i^\circ$ in null and space-like directions. These matching conditions are quite weak but suffice to reduce the asymptotic symmetry group to a Poincar\'e group $\mathfrak{p}_{i^\circ}$. Restriction of $\mathfrak{p}_{i^\circ}$ to future null infinity $\mathscr{I}^{+}$ yields the canonical Poincar\'e subgroup $\mathfrak{p}^{\rm bms}_{i^\circ}$ of the BMS group $\mathfrak{B}$ selected in the companion paper and its restriction to spatial infinity $i^\circ$ gives the canonical subgroup $\mathfrak{p}^{\rm spi}_{i^\circ}$ of the Spi group $\mathfrak{S}$ there. As a result, one can meaningfully compare angular momentum that has been defined at $i^\circ$ using $\mathfrak{p}^{\rm spi}_{i^\circ}$ with that defined on $\mathscr{I}^{+}$ using $\mathfrak{p}^{\rm bms}_{i^\circ}$. We show that the angular momentum charge at $i^\circ$ equals the sum of the angular momentum charge at any 2-sphere cross-section $S$ of $\mathscr{I}^{+}$ and the total flux of angular momentum radiated across the portion of $\mathscr{I}^{+}$ to the past of $S$. In general the balance law holds only when angular momentum refers to ${\rm SO(3)}$ subgroups of the Poincar\'e group $\mathfrak{p}_{i^\circ}$. Comment: Version to appear in JHEP. Slightly edited to improve the presentation. Four references added. 30 pages, 1 figure |
| Databáze: | arXiv |
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