广义Witten方程的准定域引力angular momentum和质心
Quasi-local gravitational angular momentum and centre of mass from generalised Witten equations
摘要：
Witten对ADM质量的正性的证明给出了三面旋量的能量定义。在本文中，我们给出了一个推广的其余六个庞加莱收费在类空无限远，这是角动量和质心。该构造改进了由Shaw引入的某些三曲面旋量方程。我们解决这些方程的渐近获得的10庞加莱收费作为积分的Nester-Witten两个形式。我们指出，定义的微分方程可以扩展到三个表面的任意签名，我们研究他们的整个边界上的一个紧凑的四维区域的时空。由此产生的准本地表达式的能量和角动量的积分在二维横截面的边界。对于任何两个连续的这样的横截面，守恒定律的推导，确定流入（流出）的物质和引力辐射。
英文摘要：
Witten's proof for the positivity of the ADM mass gives a definition of energy in terms of three-surface spinors. In this paper, we give a generalisation for the remaining six Poincaré charges at spacelike infinity, which are the angular momentum and centre of mass. The construction improves on certain three-surface spinor equations introduced by Shaw. We solve these equations asymptotically obtaining the ten Poincaré charges as integrals over the Nester--Witten two-form. We point out that the defining differential equations can be extended to three-surfaces of arbitrary signature and we study them on the entire boundary of a compact four-dimensional region of spacetime. The resulting quasi-local expressions for energy and angular momentum are integrals over a two-dimensional cross-section of the boundary. For any two consecutive such cross-sections, conservation laws are derived that determine the influx (outflow) of matter and gravitational radiation.
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