论文标题
旋转penrose不平等的方法
A Spinor Approach to Penrose Inequality
论文作者
论文摘要
考虑一个渐近的欧几里得初始数据集，其边缘略微捕获的表面（可能是未来和过去的多连接组件的结合）作为内部边界。通过对正能定理基础的旋转框架的进一步发展，制定了精致的维滕身份，在最大切片案例中，揭示了身份与Yamabe类型的形式不变性的密切联系。从共同的几何学角度来看，对Sen-Witten操作员的Kato-Yau不平等也得到了证明。在旋转框架基础的汉密尔顿图片的指导下，penrose类型的不平等现象得到证明，鉴于鉴于主要能量条件的效果，ADM能量momentum的非零常数小于统一的非零常数，并受到边缘捕获表面的面积半径的限制。为了完全普遍地建立Penrose不等式，就足以证明Sen-Witten Spinor的标准，即受到适当定义的最外面略微捕获的表面的APS边界条件，在下面是Schwarzschschild Metric所获得的。
Consider an asymptotically Euclidean initial data set with a smooth marginally trapped surface (possibly a union of future and past multi-connected components) as inner boundary. By a further development of the spinorial framework underlying the positive energy theorem, a refined Witten identity is worked out and in the maximal slicing case, a close connection of the identity with a conformal invariant of Yamabe type is revealed. A Kato-Yau inequality for the Sen-Witten operator is also proven from a conformal geometry perspective. Guided by the Hamiltonian picture underlying the spinorial framework, a Penrose type inequality is then proven to the effect that given the dominant energy condition, the ADM energy-momentum is, up to a non-zero constant less than unity, bounded by the areal radius of the marginally trapped surface. To establish the Penrose inequality in full generality, it is then sufficient to show that the norm of the Sen-Witten spinor, subject to the APS boundary condition imposed on a suitably defined outermost marginally trapped surface, is bounded below by that attained in the Schwarzschild metric.
