black hole spacetimes | vanishing angular momentum | positive angular momentum |
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vanishing charge | Schwarzschild spacetime | Kerr spacetime |
positive charge | Reissner-Nordstrom spacetime | Kerr-Newman spacetime |
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In classical gravity (general relativity) the positive energy theorem (formerly the positive mass conjecture) states that under reasonable assumptions (dominant energy condition) on the nature of the matter content (i.e. on the non-gravitational stress-energy tensor) then the ADM mass of any asymptotically flat spacetime solving the Einstein equations is non-negative, and zero precisely only for Minkowski spacetime (the vacuum).
An influential argument for the positive energy theorem for supergravity is due to
The first proof of the positive energy theorem for bosonic Einstein gravity was given in
Richard Schoen and Shing-Tung Yau, On the proof of the positive mass conjecture in general relativity, Commun. Math. Phys. 65, 45 (1979).
Richard Schoen and Shing-Tung Yau, Proof of the positive mass theorem. II, Commun. Math. Phys. 79, 231 (1981).
An alternative proof for Einstein gravity, making crucial use of spinor algebra, was found in
Comparison of the relation between the proof for supergravity and the spinorial proof for Einstein gravity is made in
See also
Maung Min-Oo, Scalar curvature rigidity of certain symmetric spaces, 1995 (pdf)
Wikipedia, Positive energy theorem
Last revised on December 13, 2016 at 14:35:06. See the history of this page for a list of all contributions to it.