  We use the canonical formalism developed together with David Robinson to st=
udy the Einstein equations on a null surface. Coordinate and gauge conditions =
are introduced to fix the triad and the coordinates on the null surface. Toget=
her with the previously found constraints, these form a sufficient number of
second class constraints so that the phase space is reduced to one pair of
canonically conjugate variables: $\Ac_2\and\Sc^2$. The formalism is related to
both the Bondi-Sachs and the Newman-Penrose methods of studying the
gravitational field at null infinity. Asymptotic solutions in the vicinity of
null infinity which exclude logarithmic behavior require the connection to fall
off like $1/r^3$ after the Minkowski limit. This, of course, gives the previous
results of Bondi-Sachs and Newman-Penrose. Introducing terms which fall off
more slowly leads to logarithmic behavior which leaves null infinity intact,
allows for meaningful gravitational radiation, but the peeling theorem does not
extend to $\Psi_1$ in the terminology of Newman-Penrose. The conclusions are in
agreement with those of Chrusciel, MacCallum, and Singleton. This work was
begun as a preliminary study of a reduced phase space for quantization of
general relativity.
