Abstract
In a companion paper [1] 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° in null and space-like directions. These matching conditions are quite weak but suffice to reduce the asymptotic symmetry group to a Poincaré group \( {\mathfrak{p}}_{i{}^{\circ}} \). Restriction of \( {\mathfrak{p}}_{i{}^{\circ}} \) to future null infinity \( {\mathcal{I}}^{+} \) yields the canonical Poincaré subgroup \( {\mathfrak{p}}_{i{}^{\circ}}^{\textrm{bms}} \) of the BMS group \( \mathfrak{B} \) selected in [2, 3] and that its restriction to spatial infinity i°, the canonical subgroup \( {\mathfrak{p}}_{i{}^{\circ}}^{\textrm{spi}} \) of the Spi group \( \mathfrak{S} \) selected in [4, 5]. As a result, one can meaningfully compare angular momentum that has been defined at i° using \( {\mathfrak{p}}_{i{}^{\circ}}^{\textrm{spi}} \) with that defined on \( {\mathcal{I}}^{+} \) using \( {\mathfrak{p}}_{i{}^{\circ}}^{\textrm{bms}} \). We show that the angular momentum charge at i° equals the sum of the angular momentum charge at any 2-sphere cross-section S of \( {\mathcal{I}}^{+} \) and the total flux of angular momentum radiated across the portion of \( {\mathcal{I}}^{+} \) to the past of S. In general the balance law holds only when angular momentum refers to SO(3) subgroups of the Poincaré group \( {\mathfrak{p}}_{i{}^{\circ}} \).
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Acknowledgments
We thank Juan Kroon and especially Kartik Prabhu for discussions and Gabriele Veneziano for motivating us to work on this issue. This work was supported in part by the Eberly and Atherton research funds of Penn State and the Distinguished Visiting Research Chair program of the Perimeter Institute. N.K. is supported by the Natural Sciences and Engineering Council of Canada.
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Ashtekar, A., Khera, N. Unified treatment of null and spatial infinity IV: angular momentum at null and spatial infinity. J. High Energ. Phys. 2024, 85 (2024). https://doi.org/10.1007/JHEP01(2024)085
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DOI: https://doi.org/10.1007/JHEP01(2024)085