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The basic assumption about inescapability beyond the Event Horizon is that the necessary escape speed (orbital speed) would exceed speed of light, therefore no object can achieve it. Now, would it be possible to escape it by other means, say, by mechanical push against the gravity, through application of force without increase of speed?


First, short introduction: What is a Dyson Ring? (feel free to skip or skim this section if you know it):

Dyson Ring is a hypothetical, artificial, ring-shaped structure surrounding a massive body (e.g. a star), rotating - essentially orbiting it - rotating at speed slightly higher or lower than orbital speed necessary to maintain orbital equilibrium - state of freefall near its surface. This way, its rotation creates centripetal force simulating gravity for inhabitants. It would create a habitat much larger than any planet, given some "rim" it could hold atmosphere, and essentially is a neat sci-fi alternative for a planet - similar conditions, vastly more surface.

The one property of it is that tensile strength of its construction allows it to exist at distance from the central body (star) that is off from normal orbit matter moving at this speed would take.

Most theoretized Dyson Rings move slightly faster than needed, stretched out, with the inner side inhabited, and the Sun in zenith for all of their surface. It is possible though (if not recommended due to buckling risks) to make one that moves slower, the star's gravity not fully overcome by rotation, compressive force applied to the construction.


Now - technological problems aside - of building a Dyson Ring (not habitable and much smaller; a scientific device of ~30km radius.) and bringing it close enough to a Black Hole.

Let's imagine a Dyson Ring that can change its circumference (say, built of segments connected with expanding/contracting actuators) - and, as effect, radius within certain range - specifically between outside and inside of Schwarzschild radius of a selected Black Hole. It is also supplied with power sources that allow to vastly increase its rotary speed.

Now, with the actuators expanded the ring is placed around the black hole, outside the even horizon, rotating so fast that its segment orbit the black hole. Its angular velocity so high the linear velocity of its surface is near to speed of light. Normally the centrifugal force would tear it apart, but it remains in equilibrium with centripetal force of gravity of the black hole.

Now, actuators contract. The angular velocity rises a little, with accordance of law of conservation of momentum, but since we're at relativistic speeds, the increase of angular speed is minimal; it's mostly the ring gaining some mass.

Now, the ring is below the Event Horizon. Since at this altitude orbital speed would exceed the speed of light, any object there would quickly spiral into the black hole. Still, the ring does not, due to its own tensile strength preventing further decrease of its own radius. It moves slower than the orbital speed, but the mechanical strain overcomes the gravity. (note, while below the Event Horizon, we're still pretty far from the singularity, so the forces exerted are not yet extreme enough to cause collapse of matter, and the rapid rotation overcomes great most of the compressing gravitational force)

Expand the actuators, increase the radius of the ring - and it is forced back outside the Event Horizon, able to broadcast its findings.

Possible physically, or am I missing something?

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Once you're in the event horizon of a black hole you're in and you can't get out. No more than you can go to yesterday. Invent a time machine and you can get out of a black hole. That's what it would take. –  Michael Brown Oct 23 '13 at 10:04
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@Michael: "No, because no" is not a satisfactory explanation. If I understand correctly, the reason is escape speed would need to exceed speed of light, but escaping a gravity well is possible by other means than fast orbiting. –  SF. Oct 23 '13 at 10:09
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In this case it is not that simple. The horizon of a black hole is a null surface in spacetime. You can't go through it from one side to the other without travelling locally faster than light, by definition. It doesn't matter where the impulse comes from. It's not a question of dynamics but rather the structure of spacetime. –  Michael Brown Oct 23 '13 at 10:17
    
Essentially a duplicate of physics.stackexchange.com/q/47828/2451 –  Qmechanic Oct 23 '13 at 17:41
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As I've noted here, defining event horizons in terms of escape velocity is actually wrong, but people do it anyway because it coincidentally gets the right answer. The event horizon is defined topologically, as the surface inside of which nothing can ever escape "to infinity." –  Chris White Oct 23 '13 at 19:05
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2 Answers

up vote 2 down vote accepted

Your question is very nearly, but not quite, a duplicate of Fighting a black hole: Could a strong spherical shell inside an event horizon resist falling in to the singularity?, and the answer is the same.

The forces that hold matter together propagate at the speed of light. Once at or inside the event horizon the forces cannot propagate outwards, so they cannot resist the inwards fall of the matter. Not even if it's a spherical shell (or in your case a ring).

For a calculation to show that even light cannot resist the inwards fall within the event horizon see Why is a black hole black?.

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Could you elaborate? The accepted answer to the question you linked is awfully skimpy on details. Which forces? Does that mean atoms fall apart as the electromagnetic force (which is the fundamental force giving the macroscopic shape to all matter) fails to propagate between them? –  SF. Oct 23 '13 at 10:31
    
There is nothing to elaborate. The atoms in the matter from which your ring is made interact with each other by electromagnetic forces, and these forces travel at the speed of light. Once inside the horizon an atom cannot interact with a second atom even fractionally farther away from the singularity because that would require faster than light interactions. Therefore your ring would disintegrate, no matter how strong it was. –  John Rennie Oct 23 '13 at 10:36
    
So, what exactly happens to matter that can't interact internally? –  SF. Oct 23 '13 at 10:40
    
Every atom in the material will follow its own trajectory towards the singularity without interacting with the other atoms. In effect the matter behaves like a cloud of atomic dust. –  John Rennie Oct 23 '13 at 10:43
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@SF. You might want to keep an eye on physics.stackexchange.com/questions/81904/… as I'm suffering a sudden crisis of confidence. –  John Rennie Oct 23 '13 at 11:27
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This is one of the common fallacies when it comes to both special and general relativity.

A lot of people, when encountering SR for the first time, think that causality can be violated by using a long pole to send messages.

Similarly, it is a common thought that one can "dip" a pole into a black hole and then pull it out. After all, solid things are solid, right?

Nope. The resolution to both these paradoxes lies in our assumption that truly "rigid" bodies exist. Poles seem to be pretty rigid in our everyday experience. But they aren't completely rigid. When you push a pole, the other end does not instantaneously shift. Instead, the local region of the pole shifts, creating a small region of compression. This region of compression propagates at subluminal speeds, preserving causality.

enter image description here

When we dip such a rod into a black hole, the atoms of the material cease to exert forces on each other. Electromagnetic forces require the exchange of carrier particles. In this environment, while the outer metal may send carrier particles to the inner one (pushing it even more inwards), the reverse isn't possible anymore. So the metal loses all rigidity, becoming more like a gas (though at this point atoms don't exactly exist either). If someone on the outside tries to pull the rod out, they'll only get the half that was above the event horizon. The half that was below will have broken off and fallen.

In your case, the expanding ring will have to exert outward forces on itself to expand. However, the inner metal does not have the ability to "push" on the outer metal. So it cannot expand (and this is before we even take into account the disintegration)

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