Positive-Definite Energy Density and Global Consequences for General Relativity

An expression for energy density in general relativity is constructed starting from the viewpoint that such an expression should be represented by the generator of translations of a preferred set of space-like coordinate surfaces. The resulting expression is shown to yield a positive-definite value for the energy. It is further shown that, in conformity with one version of Mach's principle, if the total energy vanishes, the space is locally flat.