# nLab positive energy theorem

Contents

### Context

#### Gravity

gravity, supergravity

# Contents

## 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).

## References

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

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)