[Physics] Does increasing pressure, increase gravity

general-relativitygravitypressurestress-energy-momentum-tensor

This question might be a little misguided, given that I have never studied GR or quantum field theory, but…

As I understand it, dark energy is caused by negative pressure in the gravity field. Gravity relates to pressure, as it results from the stress-energy tensor? Sometimes this pressure can be negative, giving rise to dark energy that pushes the universe apart.

What about here on the surface of a planet, where there is a positive atmospheric pressure? Is this the same kind of pressure that is talked about in the context of the gravity field? And does being under pressure cause Earth's gravity to be increased as a result?

Best Answer

Yes, (positive) pressure increases gravity.

Consider an ideal gas and ask what you mean by the pressure. The pressure of a gas is the result of moving gas molecules colliding with the walls of their contained and bouncing off. The force the molecules exert on the walls of the container is simply the rate of change of their momentum as they bounce off those walls, and the rate of change of momentum is related to how fast the gas molecules are travelling - faster gas molecules = more pressure.

But faster gas molecules also means a greater kinetic energy. So if we increase the pressure of a gas (while keeping the density and volume fixed) we are increasing the total energy of the gas. And if we increase the total energy we are increasing the total mass (obtained by dividing the energy by $c^2$). And if we are increasing the total mass we are increasing the gravity that gas creates.

Admittedly this is a grossly simplified version of how pressure creates spacetime curvature, but I think it serves to give you the general idea. More precisely we should say that Einstein's equation relates the curvature to the stress-energy tensor, and the pressure makes a contribution to the diagonal entries in this tensor.

The obvious next question is what negative pressure means, and there isn't a simple picture of this like gas molecules producing a positive pressure. I explore this question a bit in my answer to 'Negative pressure' counteracting gravity?.

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