TY - JOUR

T1 - BMS Charges Without Supertranslation Ambiguity

AU - Chen, Po Ning

AU - Wang, Mu Tao

AU - Wang, Ye Kai

AU - Yau, Shing Tung

N1 - Funding Information:
P.-N. Chen is supported by NSF grant DMS-1308164 and Simons Foundation collaboration grant #584785, Y.-K. Wang is supported by MOST Taiwan grant 107-2115-M-006-001-MY2 and 109-2628-M-006-001 -MY3. This material is based upon work supported by the National Science Foundation under Grant Number DMS-1810856 and DMS-2104212 (Mu-Tao Wang).
Publisher Copyright:
© 2022, The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature.

PY - 2022/8

Y1 - 2022/8

N2 - The asymptotic symmetry of an isolated gravitating system, or the Bondi–Metzner–Sachs (BMS) group, contains an infinite-dimensional subgroup of supertranslations. Despite decades of study, the difficulties with the “supertranslation ambiguity” persisted in making sense of fundamental notions such as the angular momentum carried away by gravitational radiation. The issues of angular momentum and center of mass were resolved by the authors recently. In this paper, we address the issues for conserved charges with respect to both the classical BMS algebra and the extended BMS algebra. In particular, supertranslation ambiguity of the classical charge for the BMS algebra, as well as the extended BMS algebra, is completely identified. We then propose a new invariant charge by adding correction terms to the classical charge. With the presence of these correction terms, the new invariant charge is then shown to be free from any supertranslation ambiguity. Finally, we prove that both the classical and invariant charges for the extended BMS algebra are invariant under the boost transformations.

AB - The asymptotic symmetry of an isolated gravitating system, or the Bondi–Metzner–Sachs (BMS) group, contains an infinite-dimensional subgroup of supertranslations. Despite decades of study, the difficulties with the “supertranslation ambiguity” persisted in making sense of fundamental notions such as the angular momentum carried away by gravitational radiation. The issues of angular momentum and center of mass were resolved by the authors recently. In this paper, we address the issues for conserved charges with respect to both the classical BMS algebra and the extended BMS algebra. In particular, supertranslation ambiguity of the classical charge for the BMS algebra, as well as the extended BMS algebra, is completely identified. We then propose a new invariant charge by adding correction terms to the classical charge. With the presence of these correction terms, the new invariant charge is then shown to be free from any supertranslation ambiguity. Finally, we prove that both the classical and invariant charges for the extended BMS algebra are invariant under the boost transformations.

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U2 - 10.1007/s00220-022-04390-1

DO - 10.1007/s00220-022-04390-1

M3 - Article

AN - SCOPUS:85129734086

VL - 393

SP - 1411

EP - 1449

JO - Communications in Mathematical Physics

JF - Communications in Mathematical Physics

SN - 0010-3616

IS - 3

ER -