# Gravitational Collapse of a Cylinder

## Main Question or Discussion Point

The Schwarzschild solution to the field equations is a vacuum solution for a spherically symmetric mass and provides the Schwarzschild radius:

rs = 2Gm / c^2.

Is there a similar treatment for a cylinder that would give its radius and height as a function of mass?

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Is there a similar treatment for a cylinder that would give its radius and height as a function of mass?
I think that any cylinder that collapsed would end up as a sphere (if it was not rotating). This is basically a consequence of the "no hair theorem". The only exception *might" be a cylinder with infinite length, but for non zero density it would have infinite mass, complicating things a tad. For example, one complication is that any point on the cylinder would only be "gravitationally aware" of the other particles within its visible horizon.

I think that any cylinder that collapsed would end up as a sphere (if it was not rotating). This is basically a consequence of the "no hair theorem". The only exception *might" be a cylinder with infinite length, but for non zero density it would have infinite mass, complicating things a tad. For example, one complication is that any point on the cylinder would only be "gravitationally aware" of the other particles within its visible horizon.
That makes sense.

But before the collapse, is there a way to figure out the maximum height to diameter (H/D) ratio to form an event horizon? Imagine a square cylinder (H=D) that is on the edge of forming an event horizon. Now add the same material to increase H for a fixed D. What ratio H/D does the event horizon finally form?

PAllen
2019 Award
I think that any cylinder that collapsed would end up as a sphere (if it was not rotating). This is basically a consequence of the "no hair theorem". The only exception *might" be a cylinder with infinite length, but for non zero density it would have infinite mass, complicating things a tad. For example, one complication is that any point on the cylinder would only be "gravitationally aware" of the other particles within its visible horizon.
I think this is an unsolved question. The black hole theorem applied iff the result is a conventional black hole. If it is some other type of singularity, the no hair theorem does not apply.

JesseM