# Variability of the orbital inclination of a black hole merger?

How variable should we expect the orbital inclination of a typical black hole merger to be, relative to the galactic plane? The LIGO simulation seems to give the impression that the orbital inclination doesn’t change, but wouldn’t general relativity predict that there would be a very large precession of the perihelion? And wouldn’t the orbital inclination also precess due to the gravitational pull from the surrounding galaxy?

Asked a different way, what would the merger look like from an outside observer watching over billions of years? Would the orientation of the orbital inclination become extremely erratic, switching from horizontal to vertical and everywhere in between?

• An orbital plane depends on what orbiting object is considered. It is not a property of the black hole in itself. Do you mean the equatorial plane? It cannot change much due to angular momentum conservation. – Stéphane Rollandin Apr 4 '18 at 11:36
• I mean the orbital plane of the two black holes, where they both orbit one central point. – Paul Apr 4 '18 at 11:46
• For two isolated bodies, i.e. nothing outside the two body system is applying a force, the plane of the orbit cannot change since that would violate conservation of angular momentum. This applies to any binary system, relativistic or not. – John Rennie Apr 4 '18 at 11:55
• @JohnRennie ok I guess I need to clarify that it’s the angle of the plane of the orbit relative to the galactic plane (or some external fixed point). – Paul Apr 4 '18 at 14:30
• There is no evidence that binary orbits preferentially align themselves with the angular momentum vector of the galaxy. – Rob Jeffries Apr 4 '18 at 16:02

• In the test particle case shown in the picture the orbit will end up filling a toroidal-like region around the central black hole. How "thick" that torus is depends on the miss alignment of the spin and orbital angular momentum. The time scale for this is relatively short. The shown orbit would be about a days worth if the central object was $10^6$ solar mass black hole. – mmeent Apr 6 '18 at 6:27