Energy and volume: A proof of the positivity of ADM energy using the yamabe invariant of three-manifolds. (English) Zbl 1172.53046
Summary: We give a new proof of the positivity (non-negativity) of ADM energy using the Yamabe invariant of three-manifolds. Properly speaking, we give a new proof of the Riemannian positive energy theorem. Namely, We prove that an asymptotically flat Riemannian three-manifold with non-negative scalar curvature cannot have negative mass. 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.
MSC:
| 53C50 | Global differential geometry of Lorentz manifolds, manifolds with indefinite metrics |
| 83C20 | Classes of solutions; algebraically special solutions, metrics with symmetries for problems in general relativity and gravitational theory |
Keywords:
maximally expanding compact cosmologies; Thurston geometrization of three-manifolds Yamabe invariant; sigma constantReferences:
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