A completely different situation arises if one is considering an
initial-boundary value problem for Einstein's equations. Although
this problem has not been solved in its full generality for
Einstein's equations, it is clear that in order for the
constraints to be satisfied during evolution, some of the
boundary values have to be chosen in a special way. It is here
that the type of equations the constraints satisfy is most
important. In particular, if they also form a hyperbolic system,
then a study of its principal part at the boundary would tell
which conditions are needed to guarantee uniqueness of the
solutions, in particular the trivial solution, and so which are
the boundary conditions we must force upon the evolution system
for the dynamical fields. Since most numerical simulations are in
fact initial-boundary value problems, the problem of well
posedness and the problem of the propagation of the constraints
are central.