Asymptotic expansions are used to study outgoing gravitational radiation in an expanding, dust‐filled Friedmann universe of negative curvature. It is found that the interaction with the matter modifies the ``peeling‐off'' behavior. A quantity is defined which is interpreted as the total mass of the source and the disturbance, and which monotonically decreases as gravitational radiation is emitted. The group of coordinate transformations that preserve the asymptotic form of the metric and the boundary conditions is the same as the isometry group of the undisturbed Friedmann model. This may indicate that no physical significance attaches to the extra transformations of asymptotically flat space which are not contained in the inhomogeneous Lorentz group.

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