Perspectives on Galactic Dynamics via General Relativity
  Responses to questions, comments and criticism of our recent paper "General Relativity Resolves.." are provided. It is emphasized that our model is entirely natural to describe the dynamics of an axially symmetric galaxy and that our solution, albeit idealized, contains the essence of the problem. The discontinuity of the metric derivative on the symmetry plane is necessarily interpreted as the effect of the mathematically idealized discontinuity of the gradient of the density and is shown to be naturally connected to the distributed volume density via the Gauss divergence theorem. We present arguments to the effect that for our approximate weak field model, we can choose the physically satisfactory mass distribution without an accompanying singular mass surface layer. To support this contention, we modify our solution slightly by removing the discontinuity with a region of continuous density gradient overlapping the $z=0$ plane. The alternative of invoking a surface layer leads to the presence of a negative mass surface layer approaching the numerical value of the positive mass continuous region. This is in contradiction with the assumed stationarity of the model. We find that a test particle behaves normally as it approaches the $z=0$ plane, the acceleration being towards the direction of this plane. This is in contradiction to the negative mass layer hypothesis as negative mass would repel the test particle. Thus, further support is added to the integrity of our original model. 
F.I. Cooperstock, S. Tieu