Conserved quantities in general relativity – the view from null infinity

  • Po-Ning Chen

    University of California, Riverside, United States of America
  • Mu-Tao Wang

    Columbia University, New York, United States of America
  • Ye-Kai Wang

    National Cheng Kung University, Tainan City, Taiwan; National Taiwan University, Taipei, Taiwan
  • Shing-Tung Yau

    Tsinghua University, Beijing, China
Conserved quantities in general relativity – the view from null infinity cover
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In general relativity, an idealized distant observer is situated at future null infinity where light rays emitted from the source approach. This article concerns conserved quantities such as mass, energy-momentum, angular momentum, and center of mass at future null infinity. The classical definition of Bondi mass at future null infinity ascertains the mass radiated away in gravitational waves distinctively. However, the same question for other conserved quantities such as angular momentum has been a subtle issue since the discovery of “supertranslation ambiguity” in the 1960s. Recently, new definitions of angular momentum and center of mass were proposed by Chen–Wang–Wang–Yau (2021) and Chen–Keller–Wang–Wang–Yau (2021) and proved to be free of such ambiguity.

These new definitions arise as limits of the Chen–Wang–Yau quasilocal conserved quantities, which are based on the theory of optimal isometric embedding and quasilocal mass of Wang–Yau. It is the purpose of this note to discuss these recent developments