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Dark energy may be described as a fluid with negative pressure.

We say that this negative pressure counteracts gravity and accelerates the expansion of the Universe.

Now consider, for example, a star. Gravity contracts the star, but positive (thermal) pressure counteracts the collapse.

This makes me confused because in both cases we have gravity as an inwards force, and in both cases we have pressure counteracting gravity, however, in one case it's 'positive' and in the other it's 'negative'.

How can I reconcile this?

Qmechanic
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user12345
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    In the star the positive pressure of the matter is pushing it apart. In the universe, the negative pressure (i.e. tension) of the gravity field in which the matter sits is yanking the matter apart. – twistor59 May 11 '13 at 14:54
  • @twistor59 Mmm... your comment got me thinking. Perhaps I should avoid thinking about matter all together - it's not needed to understand D.E. In a Universe with only D.E., there will be accelerated expansion, but crucially it seems that the pressure is 'outward', which naturally suggests 'positive'. – user12345 May 11 '13 at 15:06
  • In fact, with high enough "positive" pressures inside a star, the gravitational attraction from pressure will be greater than the repulsion from the pressure gradient. This helps in setting theoretical upper limits to masses of neutron stars. –  May 11 '13 at 16:26

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Imagine you have a star sized ball of gas that is in equilibrium i.e. the pressure of the gas exactly balances the inwards gravitational force. Now imagine compressing the gas. This has two effects:

The first effect is the obvious one that compressing the gas increases the pressure, so the result is an outward force and if we stop compressing the gas we expect it to expand again. This is the standard Boyle's law behaviour that we all learned in school.

The second effect arises from general relativity. By compressing the gas we have done work on it, so the gas/star now has more energy than it did before. But in GR energy causes curvature just like mass does. In fact the stress energy tensor doesn't distinguish between mass and energy - it uses a single value for mass/energy density using the famous formula $E = mc^2$ to equate the two. So by compressing the gas we have increased the spacetime curvature caused by the star so we have made it's gravitational field stronger.

Under most circumstances the increase in the gravity caused by pressure is insignificant, and pressure has the effect we expect i.e. it causes the star to expand. However in extreme cases, like the neutron star collapse mentioned by Chris in his comment, the gravitation effect of pressure overcomes its effect on expansion and pressure then contributes to the collapse.

Dark energy is rather different. I started by pointing out that by compressing the gas and increasing the pressure we are doing work on the gas/star and this contributes to its gravity. If you take some region of vacuum containing just dark energy and compress it the dark energy does work on you i.e. the energy of the space you've compressed decreases. This is what we mean by a negative pressure. Because of this dark energy can't cause attraction in the way that pressure can.

John Rennie
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  • I guess I was confused with the definition of pressure. So, the key point is to avoid thinking of 'outward pressure vs. inward gravity' (i.e. the star analogy) but rather to think of $T_{\mu\nu}$. I.e., pressure is just a contribution to the energy, and whether its negative or not depends on how the energy changes under compression. Thanks a lot John! – user12345 May 12 '13 at 11:31
  • Dark energy is rather different. I started by pointing out that by compressing the gas and increasing the pressure we are doing work on the gas/star and this contributes to its gravity. If you take some region of vacuum containing just dark energy and compress it the dark energy does work on you i.e. the energy of the space you've compressed decreases. Wouldn't this violate 2 law of thermodynamics, and if one would expand the space he would create the additional energy and could create Perpetuum Mobile? There must be flaw in my thinking, I would appreciate if you could point it out. Thanks. – Matas Vaitkevicius Sep 10 '15 at 09:16
  • @MatasVaitkevicius: energy isn't conserved in an expanding universe – John Rennie Sep 10 '15 at 09:55
  • "In fact the stress energy tensor doesn't distinguish between mass and energy - it uses a single value for mass/energy density using the famous formula $E = m c^2$ to equate the two." This seems like an oversimplification. The stress-energy tensor doesn't just depend on mass/energy. Even when you assume that it's isotropic, it still depends on pressure. Many ways that you would store a large amount of energy, other than as rest mass, create a lot of pressure. In particular, a gas with mass $M$ compressed enough to add energy $E$ won't behave the same gravitational as a mass $M + E/c^2$. – qbt937 Sep 03 '22 at 04:18
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You should distinguish two things: the pressure itself, and the gravitation that it creates. First of all, why does it create some gravitation? Because energy does. It is not the mass of the Earth that pulls us down - it is the energy of that mass, $E=mc^2$, that makes us heavy and not flying but walking.

And the energy does that indirectly. First, it creates, "emits", a gravitational field, and next, that gravitational field tells us where to be pulled to. That is different from anything that energy could do to you directly - for example, acting directly, energy could heat you.

And the same difference holds for the pressure itself (its direct action) and its gravitational effect. For example, you can pull a spring. Then your hands would feel its tension directly. And if you stand near someone who pulls the spring, you would feel its indirect gravitational effect (it would be smaller by factor $c^{-1}$ of several orders, and it would attract or repel you from the spring).

That is what happens with the Dark Energy. It has negative pressure, and could pull us with it, but we don't feel it. It is compensated - the same way as we don't feel the atmospheric pressure, and deep sea fish does not feel the pressure too. But its indirect gravitational effect still remains. And we observe it by the overall pull of galaxies from each other.

The sign of gravitational effect is found by the sign of the usual gravitational effect of our positive masses and energies. The theory should be symmetrical with respect to time and space, and similar temporal and spatial quantities. Because of that, positive energy attracts; positive pressure attracts; and negative pressure, or pull, repels.

firtree
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  • But what causes this negative pressure in the first place? – dualredlaugh Jan 24 '16 at 07:15
  • @dualredlaugh Every theorist would like to know! But no one knows! We call it the Dark Energy because it's the only two things we know about it: it has some kind of energy, and it does not give light. Two more things, to be exact: it cannot be any kind of matter (that's why it's not called Dark Matter, and it's not included into the Dark Matter), and it is extremely uniform throughout the Universe. That's all. Beyond that, we only have guesses, and they are absolutely random. – firtree Feb 29 '16 at 08:17
  • A sufficiently negative pressure repels. – user50229 Apr 10 '20 at 21:21
  • @user50229 No, any negative pressure repels. It is just that there is rarely any pressure without energy. And positive energy attracts. So the attraction and the repulsion fight each other, subtract from each other, and the overall effect could be either attraction or repulsion. But even in the case of attraction, if you measure the attraction, you will find that some repulsion have taken place. – firtree Apr 13 '20 at 18:16
  • @firtree I meant that in the case of the star g = −4πG(ρ + 3P) so P has to be sufficently negative to make (ρ + 3P) negative and thus cause a repulsion. – user50229 Apr 14 '20 at 03:32
  • @user50229 I was talking about the same formula, – firtree Apr 17 '20 at 20:59
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Understand you could keep the "Dark Energy" (= Cosmological Constant) term where Einstein originally inserted it, on the LHS of the equation, and view it as an intrinsic part of the Curvature Tensor. If so, the "empty" space-time fabric would not be perfectly "flat" (Minkowskian) but would have an intrinsic curvature, vaguely like the intrinsic upward bowing of a flatbed trailer, which bends upward when empty so as to support heavier loads.

Would like to speculate whether perhaps the "missing polarity" of gravity (negative mass) somehow resides within the "fabric" of spacetime itself? Instead of matter possessing both polarities of charge (plus & minus, obeying "opposites attract" and "like repels like"), perhaps all matter has one polarity of mass (plus) and all spacetime fabric has the other (negative)? Perhaps, too, "like attracts like" and "opposites repel" with Gravity?

Could a spacetime fabric possessing a "material property" of "negative mass" which repels normal mass be consistent with Dark Energy?

Erik Nelson
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