Minimizing properties of critical points of quasi-local energy

Abstract

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. In particular, under a condition on the mean curvature vector we show a critical point minimizes the quasi-local energy locally. The same condition also implies that the critical point is globally minimizing among all axially symmetric embedding provided the image of the associated isometric embedding lies in a totally geodesic Euclidean 3-space.

Accepted by Comm. Math. Phys

References in corpus (3)

• Quasilocal mass in general relativity
• Isometric embeddings into the Minkowski space and new quasi-local mass
• Critical points of Wang-Yau quasi-local energy

Cited by in corpus (10)

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• Geometric Inequalities for Quasi-Local Masses
• Wang and Yau's Quasi-Local Energy for an Extreme Kerr Spacetime
• Chen-Nester-Tung quasi-local energy and Wang-Yau quasi-local mass
• Quasilocal energy and surface geometry of Kerr spacetime
• Aspects of Quasi-local energy for gravity coupled to gauge fields
• Properties of Quasi-local mass in binary black hole mergers
• Some Remarks on Wang-Yau Quasi-Local Mass
• Quasi-local mass at axially symmetric null infinity
• Strong field behavior of Wang-Yau Quasi-local energy