[Physics] Vacuum and repulsive gravity


How can one show from General Relativity that gravity is attractive force, and under which conditions it becomes repulsive, also why positive energy vacuum drives repulsive gravity?

Best Answer

The Einstein field equations actually don't say anything at all about the nature of matter. Their structure is that they relate a certain measure of spacetime curvature G to the stress-energy tensor T: $G_{ab}=8\pi T_{ab}$. The stress-energy tensor describes any matter that is present; it's zero in a vacuum. Trivially, you can write down any equations you like describing an arbitrary spacetime that you've made up, and then by calculating G you can find the T that is required in order to allow the existence of that spacetime. However, that T may have properties that are different from those of any known type of matter. T has a very specific structure for certain types of matter, such as electromagnetic radiation or "dust" (meaning a perfect fluid made of particles that have velocities $\ll c$ relative to one another). There are various conjectures, called energy conditions, about what types of stress-energy tensors are physically possible for realistic types of matter. They have names like the weak energy condition (WEC), strong energy condition (SEC), etc. The WEC amounts to a statement that the energy density is never negative in any frame of reference. If it was violated, then you could get repulsive gravity. Basically all energy conditions are known to be violated under some circumstances. Here is a nice discussion of that: http://arxiv.org/abs/gr-qc/0205066

The cosmological constant is sometimes taken as a separate term in the Einstein field equations, but it can also be treated as a type of matter with a certain contribution to the stress-energy tensor. A spacetime with only a cosmological constant, and nothing else in it, violates various energy conditions.