TY - JOUR

T1 - Some estimates of Wang-Yau quasilocal energy

AU - Miao, Pengzi

AU - Tam, Luen Fai

AU - Xie, Naqing

N1 - Publisher Copyright:
© 2009 IOP Publishing Ltd.
Copyright:
Copyright 2015 Elsevier B.V., All rights reserved.

PY - 2009

Y1 - 2009

N2 - Given a spacelike 2-surface σ in a spacetime N and a constant future timelike unit vector T0 in R3,1, we derive upper and lower estimates of Wang-Yau quasilocal energy E(σ,X, T0) for a given isometric embedding X of σ into a flat 3-slice in R3,1. The quantity E(σ,X, T0) itself depends on the choice of X; however, the infimum of E(σ,X, T0) over T0 does not. In particular, when σ bounds a compact domain ω in a time symmetric 3-slice in N and has nonnegative Brown-York quasilocal mass mBY(σ, ω), our estimates show that infT0 E(σ,X, T0) equals mBY(σ, ω). We also study the spatial limit of infT0 E(Sr,Xr, T0), 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 R3 ∪ R3,1. We show that if (M, g, p) has future timelike ADM energy-momentum, then lim r→∞ infT0 E(Sr,Xr, T0) equals the ADM mass of (M, g, p).

AB - Given a spacelike 2-surface σ in a spacetime N and a constant future timelike unit vector T0 in R3,1, we derive upper and lower estimates of Wang-Yau quasilocal energy E(σ,X, T0) for a given isometric embedding X of σ into a flat 3-slice in R3,1. The quantity E(σ,X, T0) itself depends on the choice of X; however, the infimum of E(σ,X, T0) over T0 does not. In particular, when σ bounds a compact domain ω in a time symmetric 3-slice in N and has nonnegative Brown-York quasilocal mass mBY(σ, ω), our estimates show that infT0 E(σ,X, T0) equals mBY(σ, ω). We also study the spatial limit of infT0 E(Sr,Xr, T0), 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 R3 ∪ R3,1. We show that if (M, g, p) has future timelike ADM energy-momentum, then lim r→∞ infT0 E(Sr,Xr, T0) equals the ADM mass of (M, g, p).

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U2 - 10.1088/0264-9381/26/24/245017

DO - 10.1088/0264-9381/26/24/245017

M3 - Article

AN - SCOPUS:84908139935

VL - 26

JO - Classical and Quantum Gravity

JF - Classical and Quantum Gravity

SN - 0264-9381

IS - 24

M1 - 245017

ER -