  LIGO's successful detection of gravitational waves has revitalized the
theoretical understanding of the angular momentum carried away by gravitational
radiation. An infinite dimensional supertranslation ambiguity has presented an
essential difficulty for decades of study. Recent advances were made to address
and quantify the supertranslation ambiguity in the context of compact binary
coalescence. Here we present the first definition of angular momentum in
general relativity that is completely free from supertranslation ambiguity. The
new definition was derived from the limit of the quasilocal angular momentum
defined previously by the authors. A new definition of center of mass at null
infinity is also proposed and shown to be supertranslation invariant. Together
with the classical Bondi-Sachs energy-momentum, they form a complete set of
conserved quantities at null infinity that transform according to basic
physical laws.
