  We present a complete discussion of the boundary term in the action
functional of general relativity when the boundary includes null segments in
addition to the more usual timelike and spacelike segments. We confirm that
ambiguities appear in the contribution from a null segment, because it depends
on an arbitrary choice of parametrization for the generators. We also show that
similar ambiguities appear in the contribution from a codimension-two surface
at which a null segment is joined to another (spacelike, timelike, or null)
segment. The parametrization ambiguity can be tamed by insisting that the null
generators be affinely parametrized; this forces each null contribution to the
boundary action to vanish, but leaves intact the fredom to rescale the affine
parameter by a constant factor on each generator. Once a choice of
parametrization is made, the ambiguity in the joint contributions can be
eliminated by formulating well-motivated rules that ensure the additivity of
the gravitational action. Enforcing these rules, we calculate the time rate of
change of the action when it is evaluated for a so-called "Wheeler-deWitt
patch" of a black hole in asymptotically-anti de Sitter space. We recover a
number of results cited in the literature, obtained with a less complete
analysis.
