GENERAL-RELATIVISTIC SCALAR-FIELD MODELS AND ASYMPTOTIC FLATNESS

For a class of scalar fields including the massless Klein-Gordon field the general relativistic hyperboloidal initial-value problems are equ ivalent in a certain sense. By using this equivalence and conformal te chniques it is proved that the hyperboloidal initial-value problem for these scalar-fields has a unique solution which is weakly asymptotica lly flat. For data sufficiently close to data for flat spacetime there exists a smooth future null infinity and a regular future timelike in finity.