This thread was triggered by @Anonymous Vegetable 's question re. nuclear fusion. In GR, energy density (in some coordinate system) is a parameter with physical implications- it is the (0,0) element in the stress energy tensor. This is in contrast with the situation in classical mechanics, where only energy differences have physical implications. In classical mechanics, the zero point of energy was defined more or less for convenience in calculation: for gravity it was when all bodies are at infinite distance (implying negative energy for finite distances), for electromagnetism it was zero field strength (so that electric potential energy was always positive), and in chemistry, "zero enthalpy" was defined arbitrarily for each element. Post- relativity, the question of how to define the zero point becomes meaningful. Under what conditions will the (0,0) element of the Einstein tensor be zero? Can it ever be negative? I am assuming no cosmological constant.