# What is counteracting spacetime deformation?

1. Jan 14, 2009

### zonde

Hi!
I have a question concerning General relativity.
I am not familiar with tensor mathematics but as I understand lasting deformation can be achieved by applying two counteracting forces to material in different places.
If tensors are used to describe curvature of spacetime and one of the forces result from presence of matter and radiation what is the counteracting force that holds spacetime in place?

2. Jan 14, 2009

### tiny-tim

Hi zonde!

Tension (or compression or pressure) (which is not directly connected with tensors, of course ) in material is a pair of two equal and opposite counteracting forces, but those two forces are at the same place …

tension (or compression or pressure) is the diagonal part of the stress energy tensor, which also has the internal shear forces of material on the off-diagonal parts …

the Einstein curvature tensor equals the stress-energy tensor (that's Einstein's field equations , which link the cause, stress-energy, to the effect, curvature), but they don't describe the same things, they only have the same coordinates.

The direct answer to your question is that the counteracting force is the same as the original force … they come in equal and opposite pairs at every point.

3. Jan 15, 2009

### zonde

But it seems to me that you have somehow missed my question. If we talk about internal forces of body then forces "come in equal and opposite pairs at every point".
My intention however was to ask about external forces where one of the forces results from presence of matter and radiation.

4. Jan 15, 2009

### tiny-tim

I'm not following you

One side of the EFE equation is gravity, which is not a force;

the other side is stress-energy, which is an ordinary non-relativistic concept;

energy isn't a force, of course, but stress is (it's force-per-area) …

which is the force that you feel needs a counteracting force?

5. Jan 15, 2009

### zonde

Hmm ...
From wikipedia: "(Stress) is a measure of the intensity of the total internal forces acting within a body across imaginary internal surfaces, as a reaction to external applied forces and body forces."
If gravity is expressed as stress then one of external forces is produced by mass and radiation ... at least it looks this way to me. Can't comment about equations :uhh:

Force that produces stress in spacetime. Or can there be a stress if there is no external force?
Stress appears where mass and energy is located so the force must come from mass and energy ... don't know how to say otherwise.

6. Jan 15, 2009

### tiny-tim

Hi zonde!
Sorry, but physics is equations … you need to look at Einstein's field equations or you won't understand what stress has to do with it.
No, gravity is not expressed as stress, gravity is expressed as the curvature of space-time.
Force produces stress in matter … it needs an equal opposing force to do so (otherwise the matter just accelerates into the distance! ).

It is mostly matter density (the "obvious" part of the stress-energy tenosr) that causes curvature … as you'd expect, since clasically gravity is caused by matter … stress is just an extra.

Curvature is not caused by forces … rather, Einstein's field equations (look them up in the PF Library, or wikipedia ) say that the curvature tensor has the same components as the stress-energy tensor (which is made up of matter density and matter stress).