Zero rest-mass fields and the Newman-Penrose constants on flat space
Zero rest-mass fields and the Newman-Penrose constants on flat space
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DOI：
10.1063/5.0034784
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发表时间：
2020-12-01
影响因子：
1.3
通讯作者：
Kroon, J. A. Valiente
中科院分区：
文献类型：
--
作者：
Gasperin, E.;Kroon, J. A. Valiente
研究了平面空间中自旋1(电磁场)和自旋2的零静质量场及其对应的Newman-Penrose(NP)常数。这一分析的目的是澄清类空超曲面上这些场的数据与它们在未来和过去零无穷远处对应的NP常量之间的对应关系。为此，利用Friedrich的圆柱体在空间无穷远处的框架来证明，将初始数据用球谐函数和测地线空间距离Rho的幂展开到空间无穷远，NP常数对应于Rho中固定阶次可能的第二高球谐函数的数据。此外，对于本文所考虑的类内的一般初始数据，对于Maxwell场和自旋-2场，在未来和过去的零无穷远的NP常数之间没有自然的对应关系。然而，如果初始数据是时间对称的，那么在未来和过去的零无穷远的NP常量具有相同的信息。
Zero rest-mass fields of spin 1 (the electromagnetic field) and spin 2 propagating on flat space and their corresponding Newman-Penrose (NP) constants are studied near spatial infinity. The aim of this analysis is to clarify the correspondence between data for these fields on a spacelike hypersurface and the value of their corresponding NP constants at future and past null infinity. To do so, Friedrich's framework of the cylinder at spatial infinity is employed to show that, expanding the initial data in terms spherical harmonics and powers of the geodesic spatial distance rho to spatial infinity, the NP constants correspond to the data for the second highest possible spherical harmonic at a fixed order in rho. In addition, it is shown that for generic initial data within the class considered in this article, there is no natural correspondence between the NP constants at future and past null infinity-for both the Maxwell and spin-2 field. However, if the initial data are time-symmetric, then the NP constants at future and past null infinity have the same information.