  The boundary at $\Cal I^+$, future null infinity, for a standard static,
spherically symmetric spactime is examined for possible linear connections. Two
independent methods are employed, one for treating $\Cal I^+$ as the future
causal boundary, and one for treating it as a conformal boundary (the latter is
subsumed in the former, which is of greater generality). Both methods provide
the same result: a constellation of various possible connections, depending on
an arbitrary choice of a certain function, a sort of gauge freedom in obtaining
a natural connection on $\Cal I^+$; choosing that function to be constant (for
instance) results in a complete connection.
  Treating $\Cal I^+$ as part of the future causal boundary, the method is to
impute affine connections on null hypersurfaces going out to $\Cal I^+$, in
terms of a transverse vector field on each null hypersurface (there is much
gauge freedom on choice of the transverse vector fields). Treating $\Cal I^+$
as part of a conformal boundary, the method is to make a choice of conformal
factor that makes the boundary totally geodesic in the enveloping manifold
(there is much gauge freedom in choice of that conformal factor).
  Similar examination is made of other boundaries, such as timelike infinity
and timelike and spacelike singularities. These are much simpler, as they admit
a unique connection from a similar limiting process (i.e., no gauge freedom);
and that connection is complete.
