  A central feature of scattering amplitudes in gravity or gauge theory is the
existence of a variety of energetically soft theorems which put constraints on
the amplitudes. Celestial amplitudes which are obtained from momentum-space
amplitudes by a Mellin transform over the external particle energies cannot
obey the usual energetically soft theorems. Instead, the symmetries of the
celestial sphere imply that the scattering of conformally soft particles whose
conformal weights under the 4D Lorentz group SL(2,C) are taken to zero obey
special relations. Such conformally soft theorems have recently been found for
gauge theory. Here, I show conformally soft factorization of celestial
amplitudes for gravity and identify it as the celestial analogue of Weinberg's
soft graviton theorem.
