  We initiate the development of a horizon-based initial (or rather final)
value formalism to describe the geometry and physics of the near-horizon
spacetime: data specified on the horizon and a future ingoing null boundary
determine the near-horizon geometry. In this initial paper we restrict our
attention to spherically symmetric spacetimes made dynamic by matter fields. We
illustrate the formalism by considering a black hole interacting with a)
inward-falling, null matter (with no outward flux) and b) a massless scalar
field. The inward-falling case can be exactly solved from horizon data. For the
more involved case of the scalar field we analytically investigate the near
slowly evolving horizon regime and propose a numerical integration for the
general case.
