Extended-body motion in black hole spacetimes: What is possible?

Free fall is only approximately universal in general relativity: different extended bodies can fall in different ways, depending on their internal dynamics. Nevertheless, certain aspects of free fall arc independent of those dynamics. This paper derives universal constraints on extended-body motion which hold in all vacuum type D spacetimes. Working in the quadrupole approximation, we show that in addition to the (previously known) constraints imposed by Killing vectors, two components of the gravitational torque must vanish. Furthermore, of the ten components of a body's quadrupole moment, four arc found to be irrelevant, two can affect only the force, and the remaining four can affect both forces and torques. As an application, we consider the capabilities of a hypothetical spacecraft which controls its motion by controlling its internal structure. In the Schwarzschild spacetime, such a spacecraft can control its mass, and by doing so, it can stabilize unstable orbits, escape from bound orbits, and more-all without a rocket.