How could strange shapes affect space-time?

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How could "strange shapes" affect space-time?

To my understanding anything massive enouph to bend space and time noticeably would end up becoming a sphere due to how gravity works. But what if you could have diffrent shapes that were massive enouph to affect the universe? What if you made a cylinder shape? What if you made a squre? What if you got massive amounts of material and wrote your name into the fabric of the universe?
 

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Oh I have already put my monogram into the fabric of spacetime, so every one knows it's mine.

You question makes me wonder if an odd shapped something massive could in a sense orbit it self. ie spin, but only because of it's own gravitational field. I can't think of anything else unusual that could happen.

Why do you ask?
 
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PAllen
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To my understanding anything massive enouph to bend space and time noticeably would end up becoming a sphere due to how gravity works. But what if you could have diffrent shapes that were massive enouph to affect the universe? What if you made a cylinder shape? What if you made a squre? What if you got massive amounts of material and wrote your name into the fabric of the universe?
The fact that substantially selfgravitating are spherical is a 'real world' limitation, due to impossibility of materials supporting extreme pressure. This is as true for Newtonina gravity as GR.

If, in a thought experiment, you want to propose (stellar) massive cylinders, I think you soon run into the problem that the required degree of rigidity would force speed of sound to exceed speed of light, leading to an inconsistency. My guess is you could write mathematically consistent solutions for such an object, but it would require exotic matter that violates the positive energy conditions.
 
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atyy
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If, in a thought experiment, you want to propose (stellar) massive cylinders, I think you soon run into the problem that the required degree of rigidity would force speed of sound to exceed speed of light, leading to an inconsistency.
Speed of sound and rigidity? Cool, something else to check out. A google search was pretty general, do you (anyone) know of a good link? And does rigidity play a role in SR GR (and is it the same as density)?

Sorry for the off topic questions.
 
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  • #6
PAllen
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Speed of sound and rigidity? Cool, something else to check out. A google search was pretty general, do you (anyone) know of a good link? And does rigidity play a role in SR GR (and is it the same as density)?

Sorry for the off topic questions.
SR is inconsistent with perfect rigidity. This is covered in any reasonable book on SR. The basic issue is that displacement would have to travel at infinite speed in a rigid object. That is inconsistent with SR or GR.

The speed of sound in a body is the speed at which a displacement propagates in it. Even for something as rigid as a diamond, this speed is orders of magnitude less than the speed of light.

Rigidity has nothing to do with density.
 
  • #8
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SR is inconsistent with perfect rigidity. This is covered in any reasonable book on SR. The basic issue is that displacement would have to travel at infinite speed in a rigid object. That is inconsistent with SR or GR.

The speed of sound in a body is the speed at which a displacement propagates in it. Even for something as rigid as a diamond, this speed is orders of magnitude less than the speed of light.

Rigidity has nothing to do with density.
That's friggin cool. I never thought of sound in that way.

Two last questions, a 100 meter iron pole, you hit one end with a hammer and at the other end I feel / hear the impact. Is the speed that would be measured how fast the force travels the length of the pole?

Im guessing that gas and liquid can be described with varying degrees of rigidity since propagation happens with them too. Is that true? (lol, no more "solids" for me)
 
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PAllen
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My hypothetical thinking about massive, nonspherical objects was premature (at least for 'conceptual' models, rather than realistic ones). Besides the Atyy's link, I found the following:

http://arxiv.org/abs/gr-qc/0407037

Toward the end of this paper, they specifically discuss how degree of deviation from sphericity is limited by energy and consistency conditions. However, the show that substantially a-spheric solutions with mass and density of neutron stars are theoretically possible, meeting all energy and consitency conditions.
 
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  • #11
PAllen
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That's friggin cool. I never thought of sound in that way.

Two last questions, a 100 meter iron pole, you hit one end with a hammer and at the other end I feel / hear the impact. Is the speed that would be measured how fast the force travels the length of the pole?

Im guessing that gas and liquid can be described with varying degrees of rigidity since propagation happens with them too. Is that true? (lol, no more "solids" for me)
One doesn't usually speak of force traveling through a pole. If you hit one end your pole, the speed of sound does describe the speed with which motion of the pole propagates (as a compression wave) to the other end. This has been physically observed in rigid ceramic rods of as little as one meter in length.

Fluid and solid state modeling is not something I have significant knowledge of. If someone here can't answer, you could ask in the solid state physic forum area to what degree similar models can be used for solids, liquids, and gases. I'm thinking what you're asking is whether to some approximation you can model them all with some model that varies parameters like viscosity, elasticity, etc. such that solid, liquid, and gaseous behavior are just different regions of the parameter space. I don't know the answer to this.
 
  • #12
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Why do you ask?
I heard from a not so reliable sorce that if you made a "ring shape" in the universe and then circled around inside of that you could travel into the past and violate causeality. So I thought I would ask here for veification.
 
  • #13
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Two last questions, a 100 meter iron pole, you hit one end with a hammer and at the other end I feel / hear the impact. Is the speed that would be measured how fast the force travels the length of the pole?
Basically that is correct. Informally you describe the force as propagating along the pole as a compression wave. The speed of sound in a material is related to its rigidity. If you had a one light year long pole and the force propagated to the far end in less than one year that would violate relativity, so relativity puts a limit on the rigidity of any material.

To my understanding anything massive enouph to bend space and time noticeably would end up becoming a sphere due to how gravity works. But what if you could have diffrent shapes that were massive enouph to affect the universe? What if you made a cylinder shape? What if you made a squre? What if you got massive amounts of material and wrote your name into the fabric of the universe?
Everything massive bends space and time, even you! The word "noticeably" is vaguely defined so it would be possible to have an object that bends space and time noticeably (here defined as measurably) that is not a sphere. However, once the density goes beyond the Shwarzschild density the object will have to collapse. However if the object is spinning it will not be exactly a sphere, but more of an oblate spheroid, which is basically the shape of the Earth at sea level (fat at the Equator). Now whether you describe a black hole as a sphere or spheriod is debatable, because the event horizon might be described as a sphere but the event horizon is not considered a physical entity and the black hole itself (the massive part) is considered a point of zero volume (or a ring of zero volume in spinning Kerr black hole.)
 
  • #14


A cosmic string would be a potential 'real world' example which is a strange shape with strange consequences, don't you think?
 

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