Undergrad Is a 2-body elliptical orbit stable in GR?

[Buzz Bloom]

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?

 

[PAllen]

I don't believe any orbital system is stable in GR due to gravitational radiation. The time scale may be enormous, but all orbits decay.

 

[Jonathan Scott]

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.

Gravitational radiation does not require an elliptical orbit. It only requires that the distribution of mass changes as seen from a given direction so that at some point the masses have a maximum elongation in one direction and at some other point they have a minimum elongation in the same direction (and possibly a maximum in some other). For a pair of orbiting objects, the maximum elongation occurs twice per orbit, so the frequency of the radiation is twice the orbit frequency.

For more information, see the Wikipedia article: Gravitational wave

 

[Orodruin]

Also, orbits are not elliptical in GR - even if you neglect the gravitational radiation. The postdiction of Mercury's orbital precession was one of the first strong hints for GR.