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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 equivalent in a certain sense. By using this equivalence and conformal techniques it is proved that the hyperboloidal initial-value problem for these scalar-fields has a unique solution which is weakly asymptotically flat. For data sufficiently close to data for flat spacetime there exists a smooth future null infinity and a regular future timelike infinity.