  In this paper we define the radiation field for the wave equation on the
Schwarzschild black hole spacetime. In this context it has two components: the
rescaled restriction of the time derivative of a solution to null infinity and
to the event horizon. In the process, we establish some regularity properties
of solutions of the wave equation on the spacetime. In particular, we prove
that the regularity of the solution across the event horizon and across null
infinity is determined by the regularity and decay rate of the initial data at
the event horizon and at infinity. We also show that the radiation field is
unitary with respect to the conserved energy and prove support theorems for
each piece of the radiation field.
