On Second Variation of Wang–Yau Quasi-Local Energy
On Second Variation of Wang–Yau Quasi-Local Energy
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DOI：
10.1007/s00023-013-0279-z
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发表时间：
2013-01
期刊：
影响因子：
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通讯作者：
P. Miao;Luen-Fai Tam
中科院分区：
文献类型：
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作者：
P. Miao;Luen-Fai Tam
我们研究非负标量曲率的紧致黎曼 3 流形边界上的泛函。泛函是广义相对论中王-丘准局域能量的第二个变体。我们证明泛函在大坐标球上是正定的，并且在近圆形表面上更普遍，包括具有正质量的渐近平坦 3 流形中的大常平均曲率球；在非负标量曲率的黎曼 3-流形中，它在中心不具有消失曲率的小测地线球上也是正定的。我们还给出了函数 H 的例子，它可以在标准 2-球体上任意接近 2，使得三元组具有正的 Brown-York 质量，而相关函数在某处为负。
We study a functional on the boundary of a compact Riemannian 3-manifold of nonnegative scalar curvature. The functional arises as the second variation of the Wang–Yau quasi-local energy in general relativity. We prove that the functional is positive definite on large coordinate spheres, and more general on nearly round surfaces including large constant mean curvature spheres in asymptotically flat 3-manifolds with positive mass; it is also positive definite on small geodesics spheres, whose centers do not have vanishing curvature, in Riemannian 3-manifolds of nonnegative scalar curvature. We also give examples of functionsH, which can be made arbitrarily close to 2, on the standard 2-spheresuch that the triplehas positive Brown–York mass while the associated functional is negative somewhere.