# The motivation of positive mass theorem

I have read some papers on positive mass theorem, mainly those by Schoen and Yau. I am awed by their minimal surface technique. Yet, I found little information about the motivation of this conjecture. Is it simply because we suppose mass in a naive sense must not be negative? Why scalar curvature makes sense to determine positivity of mass?

Thank you!

The motivation of course comes from physics: under suitable simplifying assumptions, a Lorentzian spacetime is locally $(M \times \mathbb R,g - dt^2)$ for $(M,g)$ a Riemannian 3-manifold, and the local mass density $T_{tt}$ of the stress-energy tensor is equal to the scalar curvature of $g$. Thus the assumption of non-negative scalar curvature of $(M,g)$ in the the positive mass theorem corresponds to the weak energy condition for the spacetime. In colloquial terms, the total energy must be non-negative if the local energy density is non-negative everywhere.