In the midst of a fun conversation about cosmological phenomena (and observability, and Objectivism, and the Rapture) with Zac and Erik today at lunch, I remembered some stuff about black holes and particularly rotating black holes doing something funky. So, when I got back to a computer, I investigated – indeed, there is a phenomenon called frame dragging predicted by general relativity. It’s kind of like the fact that space can rotate if enough mass is applied, because the massive object bends spacetime. This has a peculiar effect on bodies in the vicinity of the rotating mass, and it is clearest from the rotating solution for a black hole, called the Kerr Metric after Roy Kerr, who found this particular solution to Einstein’s field equations.
So how do black holes work? When an object is so massive that the structure of the object can’t resist the force of gravity causing it to implode, and if the mass is large enough, no force is sufficient to prevent its collapse to a singularity – a point in space, that’s like a rip in spacetime. The region surrounding a singularity is bounded by an event horizon – within this region, light can’t escape the pull of gravity from the singularity. But when the singularity is rotating (that is, the body that collapsed but had large angular momentum – rotational energy), it generates TWO horizons – the static event horizon, and the ergosphere, an ellipsoid region of frame dragging surrounding the spherical horizon of the singularity.
The ergosphere’s boundary is the point at which space is dragged around at the speed of light. But in between that and the event horizon, space is being dragged at MORE than the speed of light – so all objects within that volume must co-rotate with the singularity. They actually gain energy and can emit into the outside universe (since they are outside the event horizon), hence the name: ergo = work. Incredibly crazy and cool, and only one of the crazy properties of the Kerr Metric solution: it can also allow for time travel (a closed timelike curve).
Anyway, I thought to myself, I should flex some real physics muscles and derive these results myself, but uh, I was unable to. Just looking at the equations involved and the number of coordinate transforms being invoked makes my head spin. Super cool though!