I Rotating Black Hole w/ Ring: Spacetime Effects

[A Puzzlement]

What would spacetime look like near a black hole that was rotating at its extremal speed and had a ring of matter orbiting it at ultra-relativistic speeds (just outside the photon sphere), such that the ring was orbiting in the same direction as the black hole’s rotation?

The ring would add to the frame-dragging effect already present due to the black hole’s own rotation. If the ring was massive enough, could this lead to the event horizon disappearing and the formation of a naked singularity or wormhole?

I was thinking a Kardashev III civilization might be able to build such a ring around its galaxy’s black hole. Maybe we should keep our eyes peeled.

 

[PeterDonis]

The ring would add to the frame-dragging effect already present due to the black hole’s own rotation.

This is a reasonable heuristic guess, but AFAIK there is no known solution to the Einstein Field Equation that actually describes this. Someone might have done a numerical simulation of it, but I'm not aware of any.

If the ring was massive enough, could this lead to the event horizon disappearing and the formation of a naked singularity or wormhole?

Again, since we have no known exact solution or numerical simulation, the best we can do is a heuristic guess. My heuristic guess would be no, because of the general rule that you can't take a near-extremal rotating hole and make it extremal or super-extremal; to do that, you would have to increase the hole's spin, but any process that increases the spin of a near-extremal hole increases its mass also, by at least enough to keep it from becoming extremal or super-extremal.

 

[sweet springs]

I wonder such a ultrarelativistic and massive ring becomes a black hole itself.

 

[A Puzzlement]

Yeah, that’s why I came up with the idea of the orbiting ring as a kind of loophole. Since the ring isn’t technically part of the black hole, the super-extremality problem is avoided.

However, like you mentioned, we need someone to actually find a solution to the equations for this system. Hopefully there’s someone willing to take a stab at it. It seems like an interesting possibility to investigate.

I could imagine sci-fi stories involving such a ring.

 

[A Puzzlement]

I wonder such a ultrarelativistic and massive ring becomes a black hole itself.

A ring-shaped black hole orbiting another black hole? Interesting!

 

[PeterDonis]

I wonder such a ultrarelativistic and massive ring becomes a black hole itself.

If it did, it would amount to the ring being swallowed by the rotating hole, increasing the rotating hole's size.

A ring-shaped black hole orbiting another black hole? Interesting!

No, that's not what would happen. A ring-shaped black hole is impossible. What would happen is described above.

 

[A Puzzlement]

If the black hole is already extremal or nearly so, and the ring is orbiting fast enough, the black hole won’t be able to absorb the ring since then the result would be a super-extremal black hole. The only way the ring could be absorbed would be if it lost some of its angular momentum.

 

[PeterDonis]

If the black hole is already extremal or nearly so, and the ring is orbiting fast enough, the black hole won’t be able to absorb the ring since then the result would be a super-extremal black hole.

No, because the ring has mass (energy) as well as angular momentum. I strongly suggest that you run some numbers instead of guessing.