If the accretion disk is on the (x,y) plane of an orthogonal reference frame what happens to objects outside the (x,y) plane (e.g. objects on the z-axis) ? In other words why is the accretion disk a disk and not a sphere (as space in 3D). Thank you. Twelvetones
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Unless the accretion disk is very heavy objects will orbit the black hole normally. Objects on the z-axis will fall in, orbit, or escape depending on their velocities. This is true both for stationary and rotating black holes.
Why is the disk flat? The answer is to some extent the same as why the planets and asteroids of the solar system are mostly confined to the ecliptic plane. A 3D cloud orbiting a mass that has some overall rotation will tend to flatten into a plane orthogonal to the rotation axis. This is because gas and particles randomly interact, exchanging momentum. Orbits in the plane are stable since they on average gain equal momentum up and down, while orbits intersecting the plane will on average tend to lose z-velocity and their inclination is reduced. One can say the disk is held up by centrifugal force, while there is no force except gravity along the z-axis.
For normal accretion disks near black holes they also have sources like nearby stars, that send streams of gas spiralling inwards (the spiralling is due to friction losses; without it the gas would just orbit). Since they have a single source that orbits, that sets up a particular plane.
Note that the rotation axis of the black hole and the accretion disk do not have to be aligned.
Anders Sandberg
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