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As a thought experiment imagine an incredibly strong spherical shell with a diameter a bit smaller than the event horizon of a particular large black hole. The shell is split into two hemispheres, and the two hemispheres are released from either side of the black hole such that they will meet and join inside the event horizon, forming a stationary uniform shell around the singularity. Of course, we consider that the shell is flawless, and exactly centred around a stationary singularity - clearly this is an unstable equilibrium but we imagine it is possible.

Is is possible that the structural forces provided by such a shell could be strong enough to resist the extreme gravity conditions inside the event horizon, and hence avoid being sucked into the singularity?

(For the purposes of this question we can consider taking the shell to extreme levels of strength, e.g. consider that the shell is made from a theoretical maximally densely packed neutronium-like material that is strongly resistant to any further compression due to the Pauli exclusion principle).

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No more than a strong spherical shell elsewhere could resist time passing. What happens at the event horizon of a black hole is much more profound then just strong gravity. –  dmckee Dec 29 '12 at 5:41
@dmckee that would make a good answer :-) –  David Z Dec 29 '12 at 5:42
@DavidZaslavsky But I'm heading to bed and don't want to write a real answer. Someone else can riff off of the comment to build a real one if they want. –  dmckee Dec 29 '12 at 5:44
in addition to @dmckee 's comment this neutronium shell will be sitting on a very metastable point. One neutron decay at the surface might destroy the symmetry and start kinematic effects that will destroy it. –  anna v Dec 29 '12 at 5:56
anna v: yes I agree it would be incredibly unstable, clearly not practical but as a thought experiment it is interesting... (well to me anyway) –  roblev Dec 29 '12 at 18:28

3 Answers 3

up vote 8 down vote accepted

As dmckee says in his comment, the answer is no, a stationary spherical shell isn't possible. This is because not even the interparticle forces in neutronium are strong enough to support it.

The problem is that once inside the event horizon there is no way to travel away from the singularity, or even maintain your distance from it, without travelling faster than light. However the fundamental forces like electromagnetism and the weak and strong forces have a maximum propagation speed of $c$, and that means the three forces cannot propagate outwards. A neutron at the outer edge of the spherical shell can't be held there because none of the three forces can move outwards to hold it there, so it must fall inwards. This applies to all the neutrons in the shell, so they and the shell must inevitably fall inwards and hit the singularity.

Proving this is a bit involved. see my answer to Why is a black hole black?, but even though I've tried to simplify the maths it's still a bit intimidating.


I've just spotted Can we have a black hole without a singularity?, which is not exactly a duplicate but is related.

Later still:

You might have noticed that dmckee said in his comment:

No more than a strong spherical shell elsewhere could resist time passing

and you might wonder what this means. Well when we talk about objects falling into black holes we generally (often without realising it) choose a set of co-ordinates called Schwarzschild co-ordinates. These are time, $t$, radial distance from the centre of the black hole, $r$, and two angular coordinates that I'll ignore for now.

As long as you're outside the event horizon $t$ and $r$ make intuitive sense. It's true that time slows down for an object near the event horizon, but we're already used to time changing for fast moving objects. Time still behaves like time and distance still behaves like distance. Specifically, we can move in either $r$ direction but we can only move forward in the $t$ direction i.e. we can't move back in time, only forward.

However, if we use our Schwarzschild coordinate system to describe events inside the event horizon we find something very odd. The $r$ coordinate that describes distance from the centre of the black hole now behaves like time, and just like time it's now only possible to move forward (towards the singularity) in $r$ and it's impossible to move backwards. This is why dmckee made the reference to the shell being unable to resist time passing. The spherical shell inside the event horizon cannot resist moving forward in $r$ any more than a spherical shell outside the event horizon can resist moving forward in $t$.

This sounds weird (it's used over and over in science fiction), but it's perfectly good physics. However I'm not fond of this viewpoint because the apparent weirdness is the result of a poor choice of coordinates. Since in the Schwarzschild coordinates an object takes infinite time to reach the event horizon you shouldn't be surprised to find the Schwarzschild coordinates do a poor job of describing what happens inside the event horizon. It's important to emphasise that if you were falling into a black hole you wouldn't experience distance behaving like time or vice versa. In your (brief!) journey to destruction at the singularity you'd find time and distance behaving just as you'd expect them to.

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Thanks, it does make sense to me that the fundamental forces cannot act on the neutrons to stop them falling further, so the shell would fall. But I wonder if there is any mileage in considering the Pauli exclusion principle further, i.e. if gravity is trying to force neutrons to occupy the same space then there could be a resistance to that movement that is different in nature to electomagnetism, strong and weak forces? –  roblev Dec 29 '12 at 18:24
One other thought... re: "the three forces cannot propagate outwards" if the shell is a thin shell then the forces do not need to propagate outwards, they need to propagate sideways. A sideways force on a collapsing atom in a shell could provide a component of resistance to the downward motion. –  roblev Jan 1 '13 at 3:54
Sadly not. A sideways force obviously has no component towards the centre. The reason arches stand up is because the forces on the blocks in them are not sideways. If you look closely at the blocks you'll find they are wedge shaped i.e. their sides are not parallel, so there is an outwards component of the apparently sideways forces on them. –  John Rennie Jan 1 '13 at 7:24

No, but that does not mean that a spherical shell could not be used as a means of keeping a black hole from expanding. Obviously, the shell would need to be quite large for most stellar black holes. The durability of material required would be inversely proportional to the durability of material involved. Meaning that, for example, a sphere of steel around a solar-mass object would need to be AT LEAST 750000000000 KM across, which is not remotely practical, even if it itself.

Even a nano-diamond sphere would need to be 750000000, 5 earth radii, across. If it were a millimeter thick, it would weigh multiple Jupiter-masses.

The only material that would have a better strength-to-weight ratio would probably be a whatever neutron stars have to support mini-mountains on their crust.

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Could expand a bit on where your numbers come from to give your answer more general value?! –  Michiel Apr 15 '13 at 6:24

some claim there is a degenerate particle and not a singularity in the center. when neutrons are pressed they form a gluon soup hyperparticle, but this requires more space because it is extra hot. So we have the creation of a degenerate particle in the center, that has a probabilistic chart non symmetrical, made of bubbles and spikes. No electron sphere can remain normal. If the neutron sphere you claim existed, it would collide even with the FIELDS THEMSELVES!

Remember, close to a black hole, the fields are greater than particles, so you can COLLIDE WITH A FIELD spontaneously! Even the particles of the walls can collide with random particles that are not in near order, because in these high energies we has spontaneously made mini tunnels. In labs we can see tunneling effect with trillions of trillions lower energy levels.

You cannot maintain a particular shape close to a black hole. All particles can spontaneously be transformed into energy. Hawkin at the beggining did claim that information is lost. Shape is a form of matter order alignment - with electromagnetic - static electricity gravity and many other effects takin' place. Leo Susskind that claimes that information is not lost, he personally teaches that looping paths may not return to some starting points, also if we multiply many times groups in maths, we cannot return to the first groups we started with. So even Susskind that supports information maintainance, he just wants that to happen, he teaches different stuff!

As we know temperature of atoms, is about different oscillating energy level layers. The best way to have atoms vibrating in accordance, is to hypercool them in the Bose-Einstein Condensate BEC. So now imagine how NOT TUNED are the atoms close in a black hole! Remember, tuning of atoms means inner time, inner spead, if atoms have huge amounts of temperature, they have so much entropy dissorder and different inner timing, that any shape not only immediately explodes, but also those particles if fast enough collide among each other so the change form!

Also many people claim that in parts of the vortex of the black hole, some parts of the vortex rotate faster than the speed of light, not as a whole the vortex, only few probabilistic parts, because of high energies.


So not only any canonical [platonic ultra regular shape] will immediately explode because of huge entropy of inner timing among particles that colliding change forms, but also the particles colide with fields, and because of huge entropy even chunks of space statistically can be relocated in huge energies.

Also if we analyse that sphere on each particle and each particle as a group of components, we loose information after many group calculations in mathematics, and we cannot recall the original order of positions.

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This stinks of quackery. –  Brandon Enright Mar 5 at 2:28

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