Current Developments in Mathematics

Volume 2021

Angular momentum and supertranslation in general relativity

Pages: 163 – 181



Mu-Tao Wang (Department of Mathematics, Columbia University, New York, N.Y., U.S.A.)


How does one measure the angular momentum carried away by gravitational radiation during the merger of a binary black hole? This has been a subtle issue since the 1960’s due to the discovery of “supertranslation ambiguity”: the angular momentums recorded by two distant observers of the same system may not be the same. In this talk, I shall describe how the theory of quasilocal mass and optimal isometric embedding identifies a new definition of angular momentum that is free of any supertranslation ambiguity. This is based on joint work with Po-Ning Chen, Jordan Keller, Ye-Kai Wang, and Shing-Tung Yau.

This material is based upon work supported by the National Science Foundation under Grant No. DMS-1810856 and DMS-2104212.

Published 2 August 2023