Evaluating quasilocal energy and solving optimal embedding equation at null infinity

Abstract

We study the limit of quasilocal energy defined in [7] and [8] for a family of spacelike 2-surfaces approaching null infinity of an asymptotically flat spacetime. It is shown that Lorentzian symmetry is recovered and an energy-momentum 4-vector is obtained. In particular, the result is consistent with the Bondi-Sachs energy-momentum at a retarded time. The quasilocal mass in [7] and [8] is defined by minimizing quasilocal energy among admissible isometric embeddings and observers. The solvability of the Euler-Lagrange equation for this variational problem is also discussed in both the asymptotically flat and asymptotically null cases. Assuming analyticity, the equation can be solved and the solution is locally minimizing in all orders. In particular, this produces an optimal reference hypersurface in the Minkowski space for the spatial or null exterior region of an asymptotically flat spacetime.

22 pages

References in corpus (3)

• Quasilocal mass in general relativity
• Isometric embeddings into the Minkowski space and new quasi-local mass
• Limit of quasilocal mass at spatial infinity

Cited by in corpus (9)

• Conserved quantities in general relativity: from the quasi-local level to spatial infinity
• BMS charges without supertranslation ambiguity
• Evolution of angular momentum and center of mass at null infinity
• Minimizing properties of critical points of quasi-local energy
• Aspects of Quasi-local energy for gravity coupled to gauge fields
• Properties of Quasi-local mass in binary black hole mergers
• Quasi-local energy in presence of gravitational radiation
• Quasi-local mass at axially symmetric null infinity
• Strong field behavior of Wang-Yau Quasi-local energy