# Elastic Limit of Spacetime?

## Main Question or Discussion Point

I understand that massive spinning objects drag spacetime along with their rotation, and that the inner region is dragged more strongly than the distant regions.

It would seem that spacetime gets stretched.

Does spacetime have an elastic limit, such that it could "break" at some point? Or is it infinitely elastic?

Could a sufficiently massive object, perhaps one that is configured like a propeller, cause something akin to cavitation of spacetime if it were to rotate sufficiently fast?

Related Astronomy and Astrophysics News on Phys.org
From what I understand, a black hole gets created when a strong enough force rips the fabric of spacetime and creates a hole of unknown depth. Here's a segment from wikipedia:

"In familiar three-dimensional gravity, the minimum energy of a microscopic black hole is 10^19 GeV, which would have to be condensed into a region on the order of the Planck length. This is far beyond the limits of any current technology."

http://en.wikipedia.org/wiki/Micro_black_hole

Drakkith
Staff Emeritus
The "stretching" of spacetime is not like a rubber band. It does not break. Stretching, bending, and other descriptions are simply us trying to turn the results of a mathematical model into something that can be communicated in a few words instead of lots and lots of math. As such they don't always translate well.

Edit: EskWIRED, please don't delete posts after you've made them unless someone hasn't replied yet. I just spent a minute or two wondering why I couldn't quote a post, only to finally figure out that you deleted it!

The "stretching" of spacetime is not like a rubber band. It does not break. Stretching, bending, and other descriptions are simply us trying to turn the results of a mathematical model into something that can be communicated in a few words instead of lots and lots of math. As such they don't always translate well.

Thanks. I keep running into conceptual problems due to reading secondary sources which are full of imprecise metaphors.

Edit: EskWIRED, please don't delete posts after you've made them unless someone hasn't replied yet. I just spent a minute or two wondering why I couldn't quote a post, only to finally figure out that you deleted it!
Oops. I didn't do that intentionally.

Drakkith
Staff Emeritus
Learning the math can help, yes. However sometimes you just have to ask the questions and get the answers, so don't feel bad. The only reason I know most of the stuff I know is because I've spent 3 years and had almost 10,000 posts on PF. I have very little formal education, and in fact, I just started up college 2 weeks ago as a freshman at the age of 29.

Chronos
Gold Member
For sure, you need to know a lot of math to grasp the 'properties' of spacetime. Analogies just don't do it justice. Einstein insisted space and time are inextricably linked to gravity. That point has never been seriously disputed. Drakkith, you're too ancient to be studying math. You may injure yourself.

Drakkith
Staff Emeritus
For sure, you need to know a lot of math to grasp the 'properties' of spacetime. Analogies just don't do it justice. Einstein insisted space and time are inextricably linked to gravity. That point has never been seriously disputed. Drakkith, you're too ancient to be studying math. You may injure yourself.
No kidding... 6 hours of math homework last night, ugh.

I understand that massive spinning objects drag spacetime along with their rotation, and that the inner region is dragged more strongly than the distant regions.

It would seem that spacetime gets stretched.

Does spacetime have an elastic limit, such that it could "break" at some point? Or is it infinitely elastic?

Could a sufficiently massive object, perhaps one that is configured like a propeller, cause something akin to cavitation of spacetime if it were to rotate sufficiently fast?
The "Fabric" representation of Space-Time is mainly used to simplify it's nature.

Space-Time "bends" in the presence of any mass, though supermassive/dense objects such as large stars, neutron stars, black holes, (quark stars?) have a more considerable effect.

This bending is known by almost all those who tackled the challenge of understanding astrophysics as Gravity.
The elasticity of the Univers is unkown hence we couldn't give you an exact answer, mainly because manifestation of pushing the Universe to the limits, also known as black holes, aren't very well understood when it comes for studying the exact singularity effect on space-time.

However we CAN say that the gravity of a black hole →∞, since the distrotion created also →∞, (the former star collapses indefinately hence it's volume →0, while it's mass retains a large value which increase overtime if the blackhole is active[Not sure about the last statement, because what happens to matter inside a black holes is unkowns so we can figure out if it actually increase in mass] density →∞.

Which brings me to my point: According to my knowledge (if incorrect please post/correct me) the elasticity limit of the Universe isn't yet known and this brings two possible answers to your question, which one is right is unkown to myself:

-If the elasticity constant of the Univers is ∞: The Universe will always bend indefinately.
-If the elasticity isn't ∞: The Universe will break under the effect of a black hole and we can postulate that matter which enter a black hole will eventually "leak" out.

Thanks for reading, and hope I didn't go too far in explaining as it's my first time around here.

Edit: As stated above by the rest, you require immense mathematical tools to solve these questions, and i'm not sure if these mathematical tools exist yet.

-If the elasticity constant of the Univers is ∞: The Universe will always bend indefinately.
-If the elasticity isn't ∞: The Universe will break under the effect of a black hole and we can postulate that matter which enter a black hole will eventually "leak" out.
I am imagining a good sized Schwarzchild black hole, where the curvature of spacetime approaches infinity near the rather large event horizon. Now I'm imagining a similar black hole, with the most significant difference being that it is rotating at a fairly fast rate, causing significant frame dragging as a result.

Given that the curvature of spacetime approaches infinity in both cases, are there no additional stresses upon spacetime in the case of the frame-dragging, rotating black hole? Is curvature the only stress or deformation or force or aspect of spacetime that changes under the influence of both gravity and frame dragging?

If so, then I understand how and why the absence of an elastic limit near a black hole would preclude an elastic limit where frame-dragging is present.

And now for something (maybe not so) completely different:

I'm trying to figure out exactly what things would seem like in a frame-dragged environment. If one were to set up a lab in such an environment, it would seem that a rotating rod tangent to the ecliptic of a massive rotating sphere would get longer and shorter as it rotates. Indeed, the center of the rod would change as well, due to one end getting longer while the other gets shorter.

It also seems that clocks attached to the ends of the rod would get faster and slower depending upon the orientation of the rod. Is that correct?

Chronos
Gold Member
What is the elasticity of 'nothing'? Space-time, to quote Einstein, does not possess ponderable properties.

I understand that massive spinning objects drag spacetime along with their rotation, and that the inner region is dragged more strongly than the distant regions.

It would seem that spacetime gets stretched.

Does spacetime have an elastic limit, such that it could "break" at some point? Or is it infinitely elastic?

Could a sufficiently massive object, perhaps one that is configured like a propeller, cause something akin to cavitation of spacetime if it were to rotate sufficiently fast?
General Relativity describes the motion of tiny "test masses." It says nothing about space. This "curved space" stuff is just an expression that is short for the curvature of the paths of test masses.

I am imagining a good sized Schwarzchild black hole, where the curvature of spacetime approaches infinity near the rather large event horizon. Now I'm imagining a similar black hole, with the most significant difference being that it is rotating at a fairly fast rate, causing significant frame dragging as a result.

Given that the curvature of spacetime approaches infinity in both cases, are there no additional stresses upon spacetime in the case of the frame-dragging, rotating black hole? Is curvature the only stress or deformation or force or aspect of spacetime that changes under the influence of both gravity and frame dragging?

If so, then I understand how and why the absence of an elastic limit near a black hole would preclude an elastic limit where frame-dragging is present.

And now for something (maybe not so) completely different:

I'm trying to figure out exactly what things would seem like in a frame-dragged environment. If one were to set up a lab in such an environment, it would seem that a rotating rod tangent to the ecliptic of a massive rotating sphere would get longer and shorter as it rotates. Indeed, the center of the rod would change as well, due to one end getting longer while the other gets shorter.

It also seems that clocks attached to the ends of the rod would get faster and slower depending upon the orientation of the rod. Is that correct?
I'm far from an expert, but the so-called curvature of space is not at all infinite at the event horizon. Indeed there is LESS curvature at the event horizon the larger the black hole. Less massive black holes have MORE curvature at the event horizon.

You could say that the curvature was infinite at the center/singularity of any black hole. I would say that the curvature there is undefined.

Maths is abstract, leaving out the messy known unknowns, and the especially messy undefined unknown unknowns. If an object doubles its volume its radius increases by an amount less than the original radius, radial increases(shell depths) follow an idealised bell curve, allowing an unlimited number of additional equal volumes, but an inflated real object(bubble) would eventually burst if its volume kept on increasing by equal amounts. Compressing an ideally elastic volume also follows the abstract bell curve below the objects surface to its maximum compression which if exceeded turns the object inside out still following the abstract bell curve.

Drakkith, you're too ancient to be studying math. You may injure yourself.
Well, I'm 56 and retiring in 10-15 years at which time I plan to finish my physics degree from being my minor (only lacked three hours from making it a dual major, but I needed a job) and take it as far as I can (masters and PhD, if possible).

I've always hated math, but, over the years, it has begun to fascinate me.

You're never too old, unless you tell yourself you are.

Maths is abstract, leaving out the messy known unknowns, and the especially messy undefined unknown unknowns. If an object doubles its volume its radius increases by an amount less than the original radius, radial increases(shell depths) follow an idealised bell curve, allowing an unlimited number of additional equal volumes, but an inflated real object(bubble) would eventually burst if its volume kept on increasing by equal amounts. Compressing an ideally elastic volume also follows the abstract bell curve below the objects surface to its maximum compression which if exceeded turns the object inside out still following the abstract bell curve.
Maybe I should have said, shell depths follow a curve of similar shape to a bell, (not statistics bell shaped curve). Shell depths are given by the original radius times cube root (1+x) - cube root(x). The google search bar draws a graph of f(x) = (1+x)^(1/3) -x^(1/3). Remember if air is removed from an inflated balloon it eventually turns inside out!

Maybe I should have said, shell depths follow a curve of similar shape to a bell, (not statistics bell shaped curve). Shell depths are given by the original radius times cube root (1+x) - cube root(x). The google search bar draws a graph of f(x) = (1+x)^(1/3) -x^(1/3). Remember if air is removed from an inflated balloon it eventually turns inside out!
As an object contracts into a singularity, maybe some of its particles turn inside out, forming new antimatter, which upon bumping into unconverted particles change into gravitons, (gravity has to get in and out somehow).

Drakkith
Staff Emeritus
As an object contracts into a singularity, maybe some of its particles turn inside out, forming new antimatter, which upon bumping into unconverted particles change into gravitons, (gravity has to get in and out somehow).
Antimatter is not simply normal matter "turned inside out". Also, gravity is the curvature of the metric of spacetime and as such it does not need to "get out" of the black hole since the black hole is also the result of the curvature of the metric.

Antimatter is not simply normal matter "turned inside out". Also, gravity is the curvature of the metric of spacetime and as such it does not need to "get out" of the black hole since the black hole is also the result of the curvature of the metric.
Thanks Drakkith, the volume of material making up the balloon does not change either, its the air pressure around the balloon that changes, causing it to inflate or deflate, or even turn inside out. Maybe as you point out, a particle that displaces a closed volume of space remains unchanged, as its displaced spacetime , surrounding it, varies.
you may like to try the graph for (1+1/sin(x))^(1/3) -(1/sin(x))^(1/3) looks like fingers & nails.

Drakkith
Staff Emeritus
What do you mean by "displaced spacetime"? Mass and energy alter the metric but nothing is displaced.

What do you mean by "displaced spacetime"? Mass and energy alter the metric but nothing is displaced.
Please see,Crank link deleted", which examines the mathematical possibility that spacetime displacements may cause a mass effect. Objects are made of molecules, atoms, and subatomic particles, which dont stay still, probably. The spacetime inside(a probability of position, determined by their standing waves) is of a different kind, to their outside surrounding spacetime, could one type displace the other?

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Drakkith
Staff Emeritus
Please see, crank link deleted, which examines the mathematical possibility that spacetime displacements may cause a mass effect. Objects are made of molecules, atoms, and subatomic particles, which dont stay still, probably. The spacetime inside(a probability of position, determined by their standing waves) is of a different kind, to their outside surrounding spacetime, could one type displace the other?
I'm sorry, that website is not a reputable source of good information. PF rules only allow discussion of mainstream theories, of which that is not.

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I'm sorry, that website is not a reputable source of good information. PF rules only allow discussion of mainstream theories, of which that is not.
Oops sorry, but in fairness you did ask about displaced spacetime, which I read about on that website. Anyway heres another fun graph for sin(x+1)^(1/3)/pi -(sin(x)/pi)^(1/3)

Oops sorry, but in fairness you did ask about displaced spacetime, which I read about on that website. Anyway heres another fun graph for sin(x+1)^(1/3)/pi -(sin(x)/pi)^(1/3)
Please note, the graph of (x+1)^(1/n) -(x)^(1/n), only continues for negative values of "x", for compressions below the objects initial volume, when the roots, of value "n", are whole, odd, real numbers. When I tried googles graph drawing aid, the even whole numbers and even plus or minus fractional numbers of "n", stopped at "x=0". Maybe this graph is an example of why its possible to turn a three dimensional shell like volume inside out, although not the shells two dimensional surface?

Please note, the graph of (x+1)^(1/n) -(x)^(1/n), only continues for negative values of "x", for compressions below the objects initial volume, when the roots, of value "n", are whole, odd, real numbers. When I tried googles graph drawing aid, the even whole numbers and even plus or minus fractional numbers of "n", stopped at "x=0". Maybe this graph is an example of why its possible to turn a three dimensional shell like volume inside out, although not the shells two dimensional surface?
Maybe of the four spacetime components making up an event happening to an object, three of them are observed along each of the objects, volumes, three " real " dimensions, while the fourth component, along an imaginary dimension, accounts for the objects, volumes, motion through an observed amount of time. Rotating objects may change the position of points of reference on an objects volumes surface, over time, eventually returning to the point of first observation, maybe spacetime only gets dragged once per revolution?