How Does Extreme Rotation Affect Space-Time Around Massive Objects?

[Justice Hunter]

So i just had a thought.

A rotating object creates a small but identifiable vortex in space-time. I would imagine that the faster the object rotates, the more drastic the vortex becomes.

My question is, if you were to have a massive object rotate very fast, at near the speed of light, how does that effect the region of space-time around it? My hypothesis is that if it spins fast enough, the vortex becomes parallel to its own rotation axis, which i guess would mean that time and space becomes infinitely slow as you approach the center of the rotating body?

A real world example i guess would be a pulsar, which rotates pretty fast, would mean that if Alice were to approach such a star, Alice would experience less time then Bob, who is at a similar star that doesn't rotate.

If this is true, then does this mean that a rotating object could essentially function like a black hole? If a small object were to be rotated fast enough, so much so that it's space-time vortex becomes parallel to its rotational axis, that light would never be able to leave the rotating body? (which i guess would make it invisible lol)

I'm curious to know what you guys think, and if I've made any wrong assumptions.

 

[Nugatory]

Google for "Kerr metric". This is the solution to the Einstein field equations in the neighborhood of a rotating spherically symmetric mass like a star or a planet.

 

[PeterDonis]

Google for "Kerr metric". This is the solution to the Einstein field equations in the neighborhood of a rotating spherically symmetric mass like a star or a planet.

Actually, strictly speaking, it's only an exact solution for a rotating black hole. It has not been proven that the Kerr metric describes the exterior of a rotating star or planet, except asymptotically (i.e., as you approach spatial infinity, the exterior metric of the rotating star/planet approaches the Kerr metric). Part of the problem is that no exact solution is known for the interior of a rotating star or planet, so there's no way to confirm that the interior solution can be matched to the Kerr metric at the surface of the object.

 

[PeterDonis]

does this mean that a rotating object could essentially function like a black hole?

No. An ordinary object simply can't be rotated fast enough; it would fly apart.

However, it is possible to have a rotating black hole, which can be thought of as a sort of "vortex" in spacetime with properties something like the ones you are thinking of (though not exactly). This is what the Kerr metric that Nugatory referred to describes.

 

[Justice Hunter]

Okay, i see, thank you for the quick references. One of the reasons i ask about this is because of this video



To save you the time from watching it, basically an experiment was done at the "University of Saint Andrews", in which they took a subatomic sphere and spun it to over 600,000,000 RPM's, and upon reaching this speed, it subsequently vanished. Saint Andrews reported it to have been "lost from the levitation trap."

Now I'm okay at maths, but the Kerr solution is a bit to complex for me, i was wondering if anyone can make sense of whether hypothetical rotating body's can actually function like a black hole without having undergone gravitational collapse?

 

[PeterDonis]

upon reaching this speed, it subsequently vanished.

That doesn't mean it turned into a black hole. It just means the trap could no longer confine it. That rotation frequency is still way short of what would be required for the surface of a subatomic object to be moving at the speed of light.

whether hypothetical rotating body's can actually function like a black hole without having undergone gravitational collapse?

No, they can't.

 

[PAllen]

A few points:

The sphere was not subatomic. It was 4 microns in diameter, similar to a virus, made of calcite. As amazing as the rpm seems, the surface speed on sphere was only 120 meters/second, no where near relativistic speed. The gravitational effect of this rotation would be totally undetectable by any conceivable method.

However, it is certainly true that a massive, compact, body with high spin distorts spacetime around it. Gravity probe B sought to measure this for earth, and just barely succeeded.

 

[Justice Hunter]

So let's just say a hypothetical object (not a black hole) could be spun till it reaches relativistic speed (without tearing itself apart). My question is what would happen to the space-time around it? would the object disappear? or would nothing special happen to it at all?

I don't understand the Kerr solution enough to really draw a conclusion from it, so i apologize if you could laymenize it that'd be great.

 

[PeterDonis]

So let's just say a hypothetical object (not a black hole) could be spun till it reaches relativistic speed (without tearing itself apart). My question is what would happen to the space-time around it?

Our best current belief is that the spacetime geometry outside it would be similar to the Kerr geometry, but without the black hole portion or the "ergosphere" region (because the surface of the object would come before we reached a small enough radius for that). However, as I said before, we don't know that for sure.

The main effect of the Kerr geometry that is different from the Schwarzschild geometry (which describes the vacuum region around a spherically symmetric, non-rotating object) is "frame dragging". See here for a description:

http://en.wikipedia.org/wiki/Frame-dragging