Witten spinor proof of the positive mass theorem (outline)
Statement
For an asymptotically flat Riemannian 3-manifold with nonnegative scalar curvature, the ADM mass is nonnegative; if the mass is zero the manifold is isometric to flat ℝ³. Witten (1981) gave a concise proof strategy using spinors and the Lichnerowicz identity on a spacelike slice; complete rigorous treatments were completed by Parker–Taubes and others. Establishes a key stability input for general relativity. Proved in ZFC once geometric hypotheses are formalized.
Source
E. Witten, A new proof of the positive energy theorem, Commun. Math. Phys. 80 (1981), 381–402; R. Schoen, S. T. Yau, On the proof of the positive mass conjecture in general relativity, Commun. Math. Phys. 65 (1979), 45–76.
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mathematics, physics
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- Theorem: Witten spinor proof of the positive mass theorem (outline)
- Proof: Witten spinor proof of the positive mass theorem (outline)