Hello, I have a probability density which in its rest frame is evenly painted upon a 2-sphere. I need to figure out how that density transforms under a Lorentz boost. Heuristically, this will consist of boosting the 2-sphere to obtain an ellipsoid of some sort, then doing a parallel projection along the boost axis back onto the sphere. At least the first part of this, I think, is a fairly standard problem since it is similar to that of calculating the beaming of synchrotron radiation. I was just wondering if anyone knows of a source that works through it so I don't have to do the whole thing from scratch. Thanks!