An Isaac Newton Institute Workshop

Einstein Constraint Equations

Why we should not take the Liu-Yau quasi-local mass seriously

Author: Niall O'Murchadha (University College, Cork)

Abstract

The Liu-Yau mass is a true mass, it is frame independent. However, the Liu-Yau mass is bigger than the Brown-York energy on any surface for which both can be defined. Further, if I take a sequence of `coordinate spheres' on any spacelike slice, both the Liu-Yau mass and the Brown-York energy asymptote to the ADM mass (which is really an energy, the `0'-th component of a Lorentz covariant 4-vector). This means that in any asymptotically flat spacetime, I can find a 2-surface with unboundedly large Liu-Yau mass. This is even true for Minkowski space.