# Elasticity of spacetime

• I
Victor Escudero

## Main Question or Discussion Point

I would like to know if it has any sense to talk about the concept of elasticity of spacetime. So, if spacetime is like a clothing that can be deformed by a big mass or a big energy, does this “clothing” has some elasticity considering for example the deformation that makes a big star in the empty?

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phinds
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I would like to know if it has any sense to talk about the concept of elasticity of spacetime. So, if spacetime is like a clothing that can be deformed by a big mass or a big energy, does this “clothing” has some elasticity considering for example the deformation that makes a big star in the empty?
No, it doesn't. In General Relativity, mass causes a "deformation" of space-time but the whole concept of a "fabric" of space or spacetime is a very unfortunate remnant of Einstein's having use that phrase before everything was well understood and it persists to this day in pop-sci presentations (but not in serious physics). We talk about "curved" space-time, for example, because we use Euclidean Geometry as our base whereas space-time is actually described by Riemann geometry (it's non-Euclidean) and things move in straight lines (called "geodesics") as defined by that geometry but they are curved when viewed from the point of view of Euclidean Geometry.

Orodruin
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space-time is actually described by Riemann geometry
To nitpick: Pseudo-Riemannian geometry or, to be more specific, Lorentzian geometry.

• dextercioby
phinds
Gold Member
2019 Award
To nitpick: Pseudo-Riemannian geometry or, to be more specific, Lorentzian geometry.
Yeah, I did learn that from some time back and I probably should just say it correctly since a beginner isn't likely to care about the distinction and it's better to be correct. Thanks.

Dale
Mentor
I would like to know if it has any sense to talk about the concept of elasticity of spacetime. So, if spacetime is like a clothing that can be deformed by a big mass or a big energy, does this “clothing” has some elasticity considering for example the deformation that makes a big star in the empty?
The "rubber sheet" analogy is pretty flawed, so you can easily get misled. The basic equation of general relativity looks something like G=kT. In that equation, T is called the stress-energy tensor and actually contains the stress tensor from Hookes law and G is the curvature which seems like a geometric distortion similar to strain. So you might be tempted to think of k as being the stiffness and G the strain, but the units don't work out. Strain is dimensionless, but curvature has units of 1/m^2, so they are different things. Similarly, in Hooke's law the stiffness is measured in Pascals, but here it is Pascal/m^2

• dextercioby
I would like to know if it has any sense to talk about the concept of elasticity of spacetime.
No, it doesn't.
What about elasticity in the sense of metric expansion of space? I'm thinking of the common balloon and ant on a rubber rope analogies.
It seems like "elasticity" would only be compatible with a bounce model and not a forever expanding model.

Last edited:
Dale
Mentor
What about elasticity in the sense of metric expansion of space?
That is part of the G I mentioned above

• stoomart
phinds