general relativity - Significances of energy conditions

I know about these different energy conditions in GR, namely strong, weak and null, but never really understood the full physical significance of them or for example how to 'derive' them or how compelling is a certain condition (for that particular one to be applied). I know that they exist because you need some constraints for $T_{\mu\nu}$ to satisfy as otherwise its completely unconstrained. Can someone please elaborate?

Answer

The energy conditions are just various possible generalizations of the statement that "energy density cannot be negative" to the whole stress-energy tensor. The reason why energy density cannot be allowed to be negative - at least in some sense - is that if arbitrary positive- and negative-energy regions were allowed, the empty vacuum would become unstable: it could spontaneously change to regions with positive energy and regions with negative energy, the the "energy density gap" would keep on growing.

We know that a condition of this kind has to hold and prevent the Universe from developing regions of a large negative energy density but we are somewhat uncertain what the precise condition satisfied by the Universe is. As I mentioned, there are many ways how to generalize the condition $T_{00}\geq 0$ to the whole tensor - one that also includes the momentum density and the fluxes of energy and momentum (the latter is the very "stress"). Do we require the energy density to be greater than zero or even the absolute value of the pressure? And so on...

The most important conditions are

• null energy condition


• dominant energy condition


• weak energy condition



• strong energy condition

See their mathematical conditions at:

http://en.wikipedia.org/wiki/Energy_condition#Mathematical_statement

It's somewhat likely that the null energy condition is indeed satisfied in the whole Universe - any macroscopic region of it - and the same may be true for the weak and dominant one (dominant one is strictly stronger than the weak one). However, one may write down models of somewhat exotic matter where the strong energy condition is violated. Although lots of "data" are known, it remains somewhat uncertain what is the precise condition that follows from the fundamental theory that knows all about the allowed types of matter - string theory. I forgot to say that all these conditions may be modified by a special treatment of the vacuum energy density coming from the cosmological constant.