FTheory: Quasilocal Mass and Isometric Embeddings
Mu-Tao Wang, Columbia University
After the great success of the positive mass theorem of Schoen-Yau and Witten, there remain challenging problems regarding the subtle notion of mass in general relativity. A fundamental difficulty is that, unlike any other physical theory, there is no density for gravitation. Thus, the total mass is no longer the bulk integral of a density function, but at best a boundary flux integral such as the ADM mass or the Bondi mass. In this talk, I shall discuss the quasi-local mass
Shing-Tung Yau and I proposed in 2009. The idea is to assign to each surface in a physical spacetime, a ``best match” in the Minkowski spacetime, by an ``optimal isometric embedding equation”, and evaluate conserved quantities, such as mass and momentum, through this reference system. If time allows, I shall discuss several applications and generalizations in joint work with Po-Ning Chen and Shing-Tung Yau.