# Is there such a thing as gravitational pressure?

1. May 8, 2010

### diagopod

I see the term once in a while, but generally not in a rigorously defined context. And when I think in terms of the gravitational force per square meter on the Earth, for example, I'm not sure it's a concept I can grasp, since gravitational force is always defined with respect to a second body. If I write the mass of the earth, times the gravitational acceleration on the earth's surface, divided by the surface of the earth, I do get a force per square meter or pressure for the earth's surface, but it seems absurdly high, and I don't think that's a valid approach anyway. Any thoughts on this would be appreciated. Thanks.

2. May 8, 2010

### thielen24

I could be way off the mark on this one, but gravitational pressure may be in reference to pressure caused by graviton particles. In the same way that photons give momentum to a solar sail (through application of a pressure/force over time). Relativistically photons have mass, however I'm not sure if the same could apply to gravitons.

3. May 8, 2010

### diazona

It'd be more correct (at least, according to modern conventions) to say that photons have energy, not mass, but also that energy acts just like mass for the purposes of gravity. (In Einstein's equation $G_{\mu\nu} = 8\pi T_{\mu\nu}$, the tensor on the right side includes both energy and mass)

Anyway, the reason photons are able to exert pressure on something like a solar sail is that they bounce off it, and so in order for momentum to be conserved, the sail has to gain (or lose) some momentum. For the same to be true of gravitons, they'd have to be able to bounce off objects, but I'm not sure I've ever heard whether such a thing is possible.

diagopod, I think in order to get meaningful information about this, you'd have to be more specific about what you mean, or at least where you're seeing the term. I'm not really sure what it might be referring to based just on what you've said here. You're right that just dividing gravitational force by surface area doesn't really tell you anything meaningful.

4. May 12, 2010

### diagopod

Thanks for all your help. Regarding context, I've seen two or three cases in which the "energy density" of the gravitational field is explored, usually as an extrapolation of the well-known equations for energy density of the electrostatic field: U = 1/2(Epsilon0)|E|^2, which would translate to U(g) = 1/2g^2/G8pi, which in turn translates into a pressure. I'll try to find a link and post it, but I found the idea interesting. In GR, is energy "stored" in the field?

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