Angular momentum to a distant observer

Abstract

In the first observation of gravitational waves GW150914 by LIGO and Virgo [1], a binary black hole of initial black hole masses 36 units and 29 units merge into a final black hole with 62 units of mass, during which exactly 3 units of mass radiated in gravitational waves. Measuring the angular momentum carried away in gravitational waves turned out to be more challenging. This has been an open problem in classical general relativity due to ``supertranslation ambiguity" since the 1960s. Two distant observers of the same system may record different amount of "radiated angular momentum". There have been a lot of efforts to resolve the supertranslation ambiguity. One approach is to find a new definition of angular momentum that would yield the same amount of radiated angular momentum for any observer. Last year, the first such ambiguity free definition of angular momentum was discovered and it is the purpose of this note to discuss this new definition.