Energy and Volume: A Proof of the Positivity of ADM Energy Using the Yamabe Invariant of Three-Manifolds

摘要

We give a new proof of the positivity (non-negativity) of ADM energy1 using the Yamabe invariant of three-manifolds. From a physical point of view, the new proof is motivated by a formula (explicitly non-negative) for the total ADM energy of emerging (asymptotically flat) stationary solutions on maximally expanding compact cosmologies. Mathematically, the proof is an application of the Thurston Geometrization of three-manifolds. Communicated by G. W. Gibbons