On the limit of Brans-Dicke theory when (omega) - (infinity)

We discuss the problem of the limit of the Brans-Dicke theory (BDT) in the limit (omega) -(infinity), when the trace of the stress tensor is not zero. It is shown that a BDT solution, with T (not equal to) 0, known in the framework of anisotropic cosmology, fails to converge to the general relativity theory (GRT) corresponding solution. Considering the spherically symmetric field problem, it is shown that the argument leading to the convergence in the static case is lost when the non-static case is considered. These remarks suggest that the non-convergence of BDT to GRT could be the general behaviour, even if T (not equal to) 0, except for some (most?) of the highly symmetric solutions, including most of the known ones. The impact on gravitational radiation detection is emphasized.