Positive-Definite Energy Density and Global Consequences for General Relativity

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Abstract
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.