Whenever the twin paradox in GR seems to be discussed, it always seems to be done in the presence of a large mass such that the twins can be considered as test particles moving in some metric. I was wondering whether the same problem could be generalised and be proposed in completely empty space in which the twins are the only things distorting the MInkowski metric? Say the twins started together at the same point in space time and then one of them did some arbitrary motion is there a way to analyse their relative proper times? It seems that the complication comes in as for one of the twins to move, they must emit matter of some kind which then distorts the metric itself. I thought perhaps you could assume that around each of the twins was a Schwarzschild metric and that you can treat the moving twin as a Kinnersley photon rocket and then stitch together the Kinnersley solution with the two Schwarzschilds to give the overall metric. Then integrate this to give proper times for both twins. Would this work and does anyone know of any work that has been done similar to this?