Up to now I had been calculating the gravitational potential arising from a collapsing galactic gas cloud, under the Holochronous model, using a numerical simulation in Excel. Obviously this is not ideal when it comes to presenting the results in a scientific publication, and I was confident that an analytical solution must exist, if only I could get me head around the concept of integrating a 4-dimensional density function. I am pleased to say that I did eventually managed to come up with the solution with nothing more than basic A-level calculus. I am still not quite sure what the underlying meaning is of the process that I have been using. It seems akin to the integration of a Lagrangian 4-density, in which case the end result driving the gravitational potential is a scalar action. Go figure! Anyway, the results agree with the simulation, which is good, and the 3 parameters of the resulting formula allow fitting of the calculated rotation curves to a wide sample of elliptical galaxy observed rotation curves, which is even better.
Just registered for the DSU conference in Bergen, Norway. With the agenda being concerned solely with Dark Matter and Dark Energy, it should be the ideal opportunity to launch my forthcoming paper on the Holochronous Universe.