Some estimates of Wang-Yau quasilocal energy

Pengzi Miao, Luen-Fai Tam, Xie Naqing

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Given a spacelike 2-surface I in a spacetime N and a constant future timelike unit vector T0 in bb R ^ 3,1 ;, we derive upper and lower estimates of Wang-Yau quasilocal energy E(I , X, T0) for a given isometric embedding X of I into a flat 3-slice in bb R ^ 3,1 ;. The quantity E(I , X, T0) itself depends on the choice of X; however, the infimum of E(I , X, T0) over T0 does not. In particular, when I bounds a compact domain I? in a time symmetric 3-slice in N and has nonnegative Brown-York quasilocal mass mathfrak m _ rm BY (Sigma,Omega );, our estimates show that inf _ T_0 E( Sigma, X,T_0); equals mathfrak m _ rm BY (Sigma,Omega );. We also study the spatial limit of inf _ T_0 E(S_r,X_r,T_0);, where Sr is a large coordinate sphere in a fixed end of an asymptotically flat initial data set (M, g, p) and Xr is an isometric embedding of Sr into mathbb R ^3 subset mathbb R ^ 3,1 ;. We show that if (M, g, p) has future timelike ADM energy-momentum, then lim _ rrightarrow infty inf _ T_0 E(S_r,X_r,T_0); equals the ADM mass of (M, g, p).
Original languageEnglish
Pages (from-to)245017 - 245029
Number of pages13
JournalClassical and Quantum Gravity
Publication statusPublished - 2009

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