Friday, April 21, 2017

dark energy - 'Negative pressure' counteracting gravity?


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?



Answer




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.


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