I understand that in a 2-body system a circular orbit is gravitationally stable in General Relativity. In Newtonian dynamics, an elliptical orbit is also stable, but is this also true in GR? I understand that the orbit precesses, but I do not intend that to change my meaning regarding stability. What prompts this question is the now documented phenomenon of a pair of black holes radiating away their mutual gravitational potential energy as gravitational waves, and ultimately collapsing together to form a single black hole. I am curious about whether this phenomenon depends on an elliptical orbit or on some other mechanism. If an elliptical orbit is unstable in GR, how does the eccentricity change during the collapse? Does it grow, shrink, or remain the same?