Minimizing properties of critical points of quasi-local energy

Understand

In relativity, the energy of a moving particle depends on the observer, and the rest mass is the minimal energy seen among all observers.

• The Wang-Yau quasi-local mass for a surface in spacetime introduced in [7] and [8] is defined by minimizing quasi-local energy associated with admissible isometric embeddings of the surface into the Minkowski space.
• A critical point of the quasi-local energy is an isometric embedding satisfying the Euler-Lagrange equation.
• In this article, we prove results regarding both local and global minimizing properties of critical points of the Wang-Yau quasi-local energy.