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On Pressure/Gravity/The Expanding Universe

  1. Feb 8, 2008 #1
    Now, It is has been derived from GR that the pressure within a substance contributes to it's gravity just as it's mass density does. But I had a thought

    Suppose you have negative pressure. A simple example I can come up with would be when a solid object is stretched to support a hanging weight.

    Would this cause a gravitational repulsion?

    And if the negative pressure was great enough, to counter the gravity substantiated by the mass density would it actually COUNTER gravity?

    And could this be why the universe is actually accelerating it's expansion, because we are full of negative pressure in areas that there is very little mass? (the universe is expanding between known points of mass i.e. galaxies).

    Now that I think about it, if this is correct, would dark energy play into this? I can't see how dark energy would have +p... And since it's gravitational effects are slim-to-none, that would give it a gravitational repulsion acting on space itself...


    Sorry for the blabbering, I'm just writing as I think.

    and looking for answers :P
  2. jcsd
  3. Feb 8, 2008 #2


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    Er... say what? If I heat a gas in a seal container to increase its pressure, can you show how this relates to the gas "gravity"?

  4. Feb 8, 2008 #3

    Specifically this section:

    The second equation states that both the energy density and the pressure causes the universe expansion rate to decrease, i.e. both cause a decceleration in the expansion of the universe. This is a consequence of gravity, with pressure playing a similar role to that of energy (or mass) density, according to the principles of general relativity. The cosmological constant, on the other hand, causes an acceleration in the expansion of the universe.
  5. Feb 8, 2008 #4
    Wikipedia probably isn't the best source to quote for a claim like this.
  6. Feb 8, 2008 #5


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    Oh dear...

    You need to make sure you understand the physics, and not simply buy the "name" being attached to such things. This isn't a thermodynamic "pressure". And you should be careful when something is being used as an analogy.

    BTW, and anyone who has been here for a while can tell you this, Wikipedia and I do not mix, i.e. I do not consider it as a valid source of reference.

  7. Feb 8, 2008 #6
    Any chance you could give me a quick round-about of what this new 'pressure' is then?

    I'd rather not wait 5 years to take a class on it >.<
  8. Feb 8, 2008 #7


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    There is a reason why, in many upper level physics courses, one needs to have the prerequisite knowledge first before taking such classes. Many of these complicated formulation require an already-established foundation and knowledge to be able to comprehend the material.

    It is unreasonable to expect that you be taught about such concepts, because inevitably, one will have to keep on backtracking to be able to explain the explanation. For example, would you know what is meant by the "flow of the stress-energy tensor" when I use it to explain to you what the pressure is in GR? What about energy density?


    You cannot learn or understand physics by bits and pieces. Physics isn't a bunch of disconnected information. This is why "learning" physics via reading Wikipedia is a fallacy, neglecting the fact that the accuracy of the information you get out of it is suspect. If you build your idea based on such information, you will also sink by it.

  9. Feb 8, 2008 #8
    I see.

    Well... perhaps I should sign up for a physics class then.
  10. Feb 8, 2008 #9
    Don't totally discount teaching yourself about it either, it's just that Wikipedia can be of limited use for a thorough education.
  11. Feb 8, 2008 #10
    If you took an elastic and stretched it, it would contain more energy than it did when there is no stress (the extra energy equals the amount you put in by working to stretch it). So, I suppose the answer to your question is no. The energy you put in would contribute toward the attractive gravitational field, as usual.

  12. Feb 8, 2008 #11
    I'm not sure what you're asking (or if you are asking seriously, since you were the one who initially steered me into the direction of GR when I needed some guidance about a year ago).

    The difference between 'dust' and a perfect fluid in GR is that the perfect fluid has pressure. Even if one models both dust and a perfect fluid of identical rest energy, the perfect fluid's gravitational field will be stronger.

    As mentioned by the OP, gravitational collapse is inevitable in dense enough material. Since the internal pressure contributes to its own gravitational field, it is a self-defeating vicious circle. More pressure leads to more gravitation, which leads to greater density, which leads to more pressure, leading to more gravitation, and so on. Schutz's book has an entire chapter dedicated to this topic, and it rocks!
    Last edited: Feb 8, 2008
  13. Feb 9, 2008 #12


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    John Baez:

    However, this does NOT mean that if you seal gas in a container and heat it, that you get extra gravity (other than from the added heat energy). You have pressure in the gas, and tension in the walls. The net result is no overall effect from the pressure terms, but they do cause a redistribution of force.
  14. Feb 9, 2008 #13
    I'm not sure why the pressure components wouldn't contribute. According to Schutz's book, momentum flux does not require a particle to cross the boundary.

    Higher random velocities is the definition of pressure in this context. From what I understand, if you add heat to a gas, its particles will move with greater random velocities.

    If the fluid's dust, the particles have no individual random movement, and that's where pressure doesn't count.
    Last edited: Feb 9, 2008
  15. Feb 10, 2008 #14
    Coming from someone who doesn't understand any of the nuances here, my understanding has always been that it's mass which produces gravity. But it does seem attractive to a lay ideation that since per Einstein and GR energy and mass are the same thing, the energy that shalayka points out to exist in a pressurized environment would also contribute to gravity? But that's a complete shot in the dark on my part.

    It also seems notable that within a given body like a star or planet increased pressure compacts the same given amount of mass into a smaller volume, thus reducing the possible distance between the given mass and other matter and increasing the r² component of the force of gravity.
  16. Feb 10, 2008 #15


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    The pressure terms in the gas do contribute. So do the tension terms in the shell enclosing the gas.

    For more details, see for instance http://en.wikipedia.org/w/index.php?title=Mass_in_general_relativity&oldid=186756158

    (sorry for using the wikipedia as a reference, but I believe the treatment is accurate. I may be biased, because I wrote much of it :-)).

  17. Feb 10, 2008 #16
    So pervect, in the case of a body like Jupiter, is the force of gravity near it greater than what can be accounted for in its conventional mass - by approximately E + ∫ 3 P dV, because it doesn't have a shell containing it?
  18. Feb 10, 2008 #17


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    No, because of an effect that I didn't mention. In flat space-time, the Komar mass of an object (which must be an isolated system) is given by (rho+3P/c^2)*volume. I've included the factors of 'c' here to show what the expression looks like in standard, non-geometric units. The space-time around Jupiter, however, is curved. Suppose we divide Jupiter up into a lot of small chunks. In each individual chunk, we adopt a coordinate system so that that chunk is in flat space-time. We do this because it's easy to explain and envision, not because it's a good way to actually carry out the calculation.

    Using this approach, the total Komar mass of jupiter is equal to the sum over chunks of

    K(ch) * volume(ch) * (rho(ch) + 3P(ch)/c^2)

    where K is the "redshift factor", computed from the metric, and is less than 1, and K(ch) indicates that K is a function of which particular chunk we are dealing with.

    See for example http://en.wikipedia.org/w/index.php?title=Komar_mass&oldid=170982833 (sorry for using a wikipedia article as a reference, especially one in which I had a hand in writing.) This also explains what I mean by "redshift factor", which you can think of as the time dilation factor of the metric. A full technical treatment can be found in Wald, "General Relativity", but will likely be much harder to follow.)

    If we take all the chunks and separate them out to infinity, the process requires work. For Jupiter this will be roughly equal to the Newtonian binding energy of the planet. Thus Jupiter weighs less than it would if we divided it up into chunks, took each chunk well away from the planet, measured the mass of each chunk, and added the measurements together.
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