  A new method is proposed for modelling spherically symmetric inhomogeneities
in the Universe. The inhomogeneities have finite size and are compensated, so
they do not exert any measurable gravitational force beyond their boundary. The
region exterior to the perturbation is represented by a
Friedmann-Robertson-Walker (FRW) Universe, which we use to study the anisotropy
in the cosmic microwave background (CMB) induced by the cluster. All
calculations are performed in a single, global coordinate system, with
nonlinear gravitational effects fully incorporated. An advantage of the gauge
choices employed here is that the resultant equations are essentially Newtonian
in form. Examination of the problem of specifying initial data shows that the
new model presented here has many advantages over `Swiss cheese' and other
models. Numerical implementation of the equations derived here is described in
a subsequent paper.
