There is no ‘rigid’ in special relativity, the best you can do is Born-rigid. Even so, its trivial to define a ball in special relativity, just define it in the frame of a corotating observer and use four vectors to move to the same collection of events in other frames You learn that a ‘ball’ in special relativity has some observer dependent properties, but thats because length and time are observer dependent in special relativity. So ‘radius’ isn’t a good concept, but ‘the radius so-and-so measures’ IS a good concept.
There is no ‘rigid’ in special relativity, the best you can do is Born-rigid. Even so, its trivial to define a ball in special relativity, just define it in the frame of a corotating observer and use four vectors to move to the same collection of events in other frames You learn that a ‘ball’ in special relativity has some observer dependent properties, but thats because length and time are observer dependent in special relativity. So ‘radius’ isn’t a good concept, but ‘the radius so-and-so measures’ IS a good concept.