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

Evaluating quasilocal energy and solving optimal embedding equation at null infinity