Constraining extended-body motion in general relativity

To a first approximation, objects in general relativity move along geodesics. Looked at more closely, a body's internal structure affects its motion, causing different objects to fall in different ways. This talk will explore what is possible and what is not in that context. For example, it is possible for a suitably-engineered spacecraft to change its orbit purely by changing its shape. Still, there are constraints. I will discuss how all such constraints arise from a very weak type of "local symmetry." Constraints arise from the presence of Killing vectors and from conformal Killing-Yano tensors, but from much more as well.