system
Given the following post, respond as if you're commenting on Reddit:
human
Can space yield?

As an engineer I work with material data in a lot of different ways. For some reason I never thought to ask, what does the material data of space or "space-time" look like?

For instance if I take a bar of aluminum and I pull on it (applying a tensile load) it will eventually yield if I pull hard enough meaning there's some permanent deformation in the bar. This means if I take the load off the bar its length is now different than before I pulled on it. 

If there are answers to some of these questions, I'm curious what they are:

* Does space experience stress and strain like conventional materials do? 

* Does it have a stiffness? Moreover, does space act like a spring, mass, damper, multiple, or none of the above?

* Can you yield space -- if there was a mass large enough (like a black hole) and it eventually dissolved, could the space have a permanent deformation like a signature that there used to be a huge mass here? 

* Can space shear?

* Can space buckle?

* Can you actually tear space? Science-fiction tells us yes, but what could that really mean? Does space have a failure stress beyond which a tear will occur?

* Is space modeled better as a solid, a fluid, or something else? As an engineer, we sort of just ignore its presence and then add in effects we're worried about.
gpt
As an engineer you're probably familiar with the concept of the stress tensor, a 3x3 matrix describing the pressures and shears on a volume. In general relativity, it is expanded to a 4x4 matrix called the stress-energy tensor, where the 2nd to 4th rows and columns are the stress tensor and the first row and column represent the time dimension. The 1,1 element is the energy density (mc^2 in a simple case), and the other time components aren't important right now.

You can look at a stress-energy tensor to see how things behave in the same way you'd look at a stress tensor to see how a material behaves. In general relativity, each different type of spacetime has a geometry that's related to the stress-energy tensor via Einstein's equations.

The simplest case is Minkowski space, or flat space. Its stress-energy tensor is just zeros. The same is true for non-flat vacuum solutions, like Schwartzschild space (around a point mass) and the hyperbolic and elliptical flat solutions: de Sitter and anti-de Sitter space.

In solutions that describe matter distributions (like the Schwarzschild interior solution for a uniform density sphere) then the stress components tell you everything you need to know.

Over large scales the universe is described by the FLRW solution. The stress-energy tensor is diagonal with the time-time component being the density of the universe and the spatial diagonal components being the isotropic pressure. In this sense, the universe behaves as a compressible gas.