  We show how matter can be included in a constrained ADM-like formulation of
the Einstein equations on constant mean curvature surfaces. Previous results on
the regularity of the equations at future null infinity are unaffected by the
addition of matter with tracefree energy-momentum tensor. Two examples are
studied in detail, a conformally coupled scalar field and a Yang-Mills field.
We first derive the equations under no symmetry assumptions and then reduce
them to spherical symmetry. Both sectors (gravitational and sphaleron) of the
spherically symmetric Yang-Mills field are included. We implement this scheme
numerically in order to study late-time tails of scalar and Yang-Mills fields
coupled to the Einstein equations. We are able to evolve spacetimes that
disperse to flat space, accrete onto a given black hole or collapse to a black
hole from regular initial data. The sphaleron sector of Yang-Mills is found to
exhibit some nontrivial gauge dynamics.
