nLab positive energy theorem

Idea

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).

Related concepts

• BPS state

References

An influential argument for the positive energy theorem for supergravity is due to

• Stanley Deser, Claudio Teitelboim, Supergravity has positive energy, Phys. Rev. Lett. 39, 249-252 (1977

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

• Edward Witten, A new proof of the positive energy theorem, Commun. Math. Phys. 80, 381 (1981).

Comparison of the relation between the proof for supergravity and the spinorial proof for Einstein gravity is made in

• Chris Hull, The positivity of gravitational energy and global supersymmetry, Comm. Math. Phys. Volume 90, Number 4 (1983), 545-561 (Euclid)

See also

• Maung Min-Oo, Scalar curvature rigidity of certain symmetric spaces, 1995 (pdf)

• Wikipedia, Positive energy theorem