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My question is simple. If we have a spaceship, whose top half is in a region of highly curved space, while the bottom half is in a region of flat space, will the top half bend in a way, which will break the ship in two?

Or will it not break, because the ship is not bending, but rather space itself is bending?

I am not concerned about how realistic it is to have such a sharp difference in curvature between two nearby regions of space. My question is IF there was such a situation, then what would happen?

Deschele Schilder
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silverrahul
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    Curvature of space time is a hypothetical approach to define force acting in a region of space, so the question does not make sense. The curved space is due to presence of gravity(most probably). Its not real but just explanation of gravity. So how could a space ship get trapped there, seriously i dont understand the question or may be it does not make sense. – Samyak Marathe Apr 27 '21 at 06:54
  • Ship does not have to get trapped there. The ship is just moving through there. I was just wondering if the structure of the ship will have to endure the push / pull forces / tidal forces when it moves through such a region. The answers seem to suggest that it would . – silverrahul Apr 27 '21 at 07:24

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The ship will break due to tidal forces. If the gravity strength is high enough then the ship will break in two where the ship crosses the surface of gravity-no-gravity. It can be of course that the difference in force (tidal force) between just inside and just outside the surface to make the ship break is already present somewhere inside the surface. In that case, the ship will break in the gravity region.

Note though that the kind of gravity field you envision isn't present in reality.

Deschele Schilder
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  • So, if i am getting this right , Then my question is simply equivalent to asking , What would happen if the head and tail of the ship are at different levels of gravity ? Is that correct, ? Because that seems a much more understandable question for me to get my head around . – silverrahul Apr 27 '21 at 07:31
  • @silverrahul Yes. When different parts of the ship experience different strengths of gravity (as is the case in your example, even if the gravity inside the separating surface is constant) then the ship can break if the difference is high enough. Note that the ship isn't stretched because space is stretched, as your second question seems to imply. – Deschele Schilder Apr 27 '21 at 07:34
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Here is what happens when there is a sharp shift in the curvature of spacetime.

First of all, those big shifts occur in the immediate vicinity of a very dense object like a neutron star or a small black hole. In either case, the curvature grows more severe the closer you (in your spacesuit) get to the object, and the difference in curvature between the end of you closest to the object- your feet, say- and the part of you furthest away (your head) is so great that your body gets pulled apart into a thin string and you die in a process called spaghettification.

So if your spaceship made a close pass to such an object, it wouldn't get broken in half- it (and its contents) would get squished into spaceship spaghetti.

Note that there isn't any process by which a portion of severely curved space can exist right next to completely flat space; the curvature difference I describe above may be extremely steep but nonetheless it is smooth rather than discontinuous.

niels nielsen
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  • " it wouldn't get broken in half- it (and its contents) would get squished into spaceship spaghetti. " Why would it get squised into spaghetti ? Do you mean it would get "stretched" into spaghetii ? and if it does get stretched into spaghetii, would the stretching , break the spaceship in half , if the material is not strong enough ? – silverrahul Apr 27 '21 at 07:09
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    It gets squished into spaghetti by what are called tidal forces, which would stretch the spaceship until it broke up into pieces, and then spaghettify the pieces all the way down to individual atoms. – niels nielsen Apr 27 '21 at 07:39
  • Okay , the answer seems to be simpler than i thought. In fact i already knew this. Essentially, in this context, what happens in different curvatures of spacetime is identical to saying what happens in different levels of gravity , right ? – silverrahul Apr 27 '21 at 08:20
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    exactly. it's what happens when there is a severe gravity gradient. – niels nielsen Apr 27 '21 at 16:26
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We have experimental evidence of what happens to matter when the curvature of space is high. Matter "melts".

So depending how high the curvature is , it will melt. I do not think nature creates curvatures of space time that are discontinuous in the way that a spaceship could be half in half out.

anna v
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  • I dont understand what you mean by melt . And , i understand that nature cannot have discontinuous curvature, my question was along the lines of what would happen in such a case. But i think the answers i am getting suggest that, having different curvatures of space has the same effect as having different levels of gravity. Is that correct ? My question was would the material of the ship experience the structural , mechanical forces of such pushing, pulling etc. . And it seems the answer is yes. Is that right ? – silverrahul Apr 27 '21 at 07:13
  • By "melts" I mean the electromagnetic bonds that keep atoms and molecules together would be overcome by the strength of the effective gravitational field , Gravitational fields are a Newtonian mechanics, curvature of space time is the the general relativity model for masses in space. For small masses and energies the formalism of GR gives small corrections, see http://www.astronomy.ohio-state.edu/~pogge/Ast162/Unit5/gps.html . For masses and energies – anna v Apr 27 '21 at 08:00
  • creating the filed large enough , you get the black hole case, again attraction as far as a mass is concerned . If you could have it half and half , it would break. – anna v Apr 27 '21 at 08:01
  • In this context, is " what happens in different curvatures of spacetime " identical to asking " what happens in different levels of gravity " ? – silverrahul Apr 27 '21 at 08:31
  • Yes, except that the Newtonian gravity (its mathematical formulation) is not adequate for the very large masses and energies where General Relativity mathematics should be used. – anna v Apr 27 '21 at 09:07
  • Yeah, i understand that the mathematical formulation and hence magnitude may be different from Newtonian one, but the effects will be qualitatively equivalent in nature, right ? – silverrahul Apr 27 '21 at 09:58
  • Newtonian cannot reproduce very highe energies and masses,, the black hole video. I linked is very far from newtonian – anna v Apr 27 '21 at 11:13
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highly curved space

In simple terms this means you have a intense gravitational field.

flat space

In equally simple terms this means very little gravitational field.

There will be a large stress between the two parts of the object if one end has a low field and one a high one. Exactly what will happen will depend on the details of those fields and the materials and structures involved. The object could compress, suffer some form of structural failure or it could survive. There's no way way to know exactly what would happen in vaguely defined circumstances.

Or will it not break, because ship is not bending, but rather the space itself is bending ?

The "bending of space" is best thought of (in this context) as a stress on the materials. We detect such stresses in the LIGO detectors which measure the changing stresses caused by gravitational waves. The stresses in spacetime cause real physical changes.

StephenG - Help Ukraine
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  • Okay, so you are saying , different curvatures of spacetime can be just thought of as different levels of gravity ? Is it that simple , i thought curvature of space had more effects than just gravity If what you are saying is true, then indeed that helps to think about what would happen, whether spaceship would break or not . In short, i think you are saying that the spaceship WOULD break, if its structure / material is not strong enough, is that correct ? – silverrahul Apr 27 '21 at 07:06
  • Curvature in GR does indeed have more to it than I'm describing, but this isn't the issue here. The issue is how do you think about the gravitational field and it's impact on materials. – StephenG - Help Ukraine Apr 27 '21 at 08:50
  • Yes, i understand there is more to curvature. But for the purposes of this question, which is just concerned with the effects of different curvatures on different parts of a spaceship, is it equivalent to the effects of different gravity at different parts of a spaceship ( kinda like tidal forces ) ? – silverrahul Apr 27 '21 at 08:52