Gravity's Impact on Box w, l, & h: Myths & Facts

[Einstein's Cat]

This question may be too unambiguous but what would the affect of a gravitational field upon a box of width, w and length, l and height, h be?

My knowledge of GR is superficial at most! I assume that the box would become elongated but why so and to what extent?

 

[jedishrfu]

Can you describe the box environment more? like is it sitting on the ground or falling into a black hole?

If falling into a black hole then it would both elongate along the direction of travel and be squeezed in every other direction not parallel to the falling direction.

https://en.wikipedia.org/wiki/Spaghettification

 

[mathman]

You need to be more specific. Unless the box is close to a black hole, there wouldn't be any noticeable affect. The forces holding the box together are generally much stronger than gravity.

 

[PeterDonis]

If falling into a black hole then it would both elongate along the direction of travel and be squeezed in every other direction not parallel to the falling direction.

This assumes the box has no internal forces holding its parts together. If it does, then stresses will be induced in the box, and the details of how its shape changes in response to tidal gravity will depend on the details of the stresses, the tensile strength of the box material, etc.

 

[Nugatory]

This question may be too unambiguous but what would the affect of a gravitational field upon a box of width, w and length, l and height, h be?

My knowledge of GR is superficial at most! I assume that the box would become elongated but why so and to what extent?

This isn't just a GR problem. It's an interesting and important problem with classical Newtonian gravity as well. In fact, understanding that classical problem is pretty much a necessary prerequisite for learning GR.

You can avoid all the complicating and unhelpful distractions about the rigidity of the box by considering an equivalent but cleaner problem. A cube has eight corners, right? Imagine that you hold eight grains of sand in space so that each is at a corner of an imaginary cube... And then let go of all of them at the same time. If there is no gravitational field present they'll just sit there, but if there is a nearby gravitating body, how do they move relative to one another?

The answer is that the four grains corresponding to the bottom face of the cube will tend to move towards one another; the four grains corresponding to the top face of the cube will also tend to move towards one another, but not quite as quickly; and the two groups of four will tend to move apart.

You should be able to work this out for yourself using Newton's $F=Gm_1m_2/r^2$. Try it - it's worth the effort. (And a hint - the gravitational force on each grain is acting in slightly different directions because the direction to the center of the gravitating body is slightly different for each grain).

 

[pervect]

This question may be too unambiguous but what would the affect of a gravitational field upon a box of width, w and length, l and height, h be?

My knowledge of GR is superficial at most! I assume that the box would become elongated but why so and to what extent?

Well, if the box is rigid, it won't change it size, by definition. There seems to be a lot of uncertanity about this point - I don't quite understand why. Rigidity is an idealization that doesn't actually exist in nature, of course - it's an idealization. But if you want to understand how gravity deforms a non-rigid box you need to basically know how strong it is - and what forces the gravity causes. This is, as others have remarked, most likely a Newtonian problem, as most of our material models for "how strong" something is are not relativistic models.

Because you're giving the spatial dimensions of the box, I'm assuming your'e interested in effects of gravity on its spatial dimension. If you're interested in other effects (gravitational time dilation comes to mind), you might want to give some more specifics.

 

[pervect]

I suppose I should add something to my original post. The existence of the idealization of rigid boxes (which I take to be Born-rigid as expressed mathematically) does have some known issues if rotation is involved. So if rigid boxes exist, by definition they cant' change their size. This is somewhat of a semantic issue though - what happens if the idealization isn't self-consistent? A full discussion would involve an existence proof of the self-consistency of the idealization.

Rotating rigid boxes (or disks) can exist, so it's not as simple as saying that such things don't exist. But it's also not necessarily as simple as saying that they always exist. There are some requirements for them to exist. This is unfortunately rather vague, but I'm not sure how to translate the Herglotz-Noether theorem into plain English.

http://arxiv.org/abs/1004.1935v3 has a highly technical discussion.

 

[Einstein's Cat]

Can you describe the box environment more? like is it sitting on the ground or falling into a black hole?

If falling into a black hole then it would both elongate along the direction of travel and be squeezed in every other direction not parallel to the falling direction.

https://en.wikipedia.org/wiki/Spaghettification

The box would contain a solitary proton and be by a black hole.