The equation of state of non-relativistic energy

[Joey21]

I just have a quick question about a concept I think I haven't fully grasped from my cosmology course.

Why does non-relativistic energy have an equation of state with w=0?
Also, is the concept of pressure different in general relativity than in thermodynamics or statistical mechanics?

 

[Orodruin]

No, it is the same concept. It is just that for normal non-relativistic matter, the pressure is negligible in comparison to the energy density. Consider an ideal gas and the pressure is going to be proportional to the temperature while the energy density is proportional to the mass of each particle. As long as the temperature is much lower than the mass, pressure is negligible (when temperature becomes comparable to mass you start reaching a relativistic gas behaving as radiation).

 

[Chalnoth]

Why does non-relativistic energy have an equation of state with w=0?

The model being used in this context is of a gas. The pressure of a gas is a function of the velocities of the individual particles that make up the gas. Those velocities have to be relativistic if the pressure is to be significant compared to the mass density.

Also, is the concept of pressure different in general relativity than in thermodynamics or statistical mechanics?

It's the exact same concept.

 

[Joey21]

Thanks for the quick replies! They will be a lot of help.