  A study is presented for the non linear evolution of a self gravitating
distribution of matter coupled to a massless scalar field. The characteristic
formulation for numerical relativity is used to follow the evolution by a
sequence of light cones open to the future. Bondian frames are used to endow
physical meaning to the matter variables and to the massless scalar field.
Asymptotic approaches to the origin and to infinity are achieved; at the
boundary surface interior and exterior solutions are matched guaranteeing the
Darmois--Lichnerowicz conditions. To show how the scheme works some numerical
models are discussed. We exemplify evolving scalar waves on the following fixed
backgrounds: A) an atmosphere between the boundary surface of an incompressible
mixtured fluid and infinity; B) a polytropic distribution matched to a
Schwarzschild exterior; C) a Schwarzschild- Schwarzschild spacetime. The
conservation of energy, the Newman--Penrose constant preservation and other
expected features are observed.

General Relativity and Quantum Cosmology