TY - JOUR

T1 - Some estimates of Wang-Yau quasilocal energy

AU - Miao, Pengzi

AU - Tam, Luen-Fai

AU - Naqing, Xie

PY - 2009

Y1 - 2009

N2 - 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).

AB - 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).

UR - http://www.ingentaconnect.com/content/iop/cqg/2009/00000026/00000024/art245017;jsessionid=xm9a6nhw3zct.alexandra

M3 - Article

VL - 26

SP - 245017

EP - 245029

JO - Classical and Quantum Gravity

JF - Classical and Quantum Gravity

SN - 0264-9381

ER -