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, the 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 highest possible spherical harmonic at fixed order in $\rho$. In addition, it is shown that the NP constants at future and past null infinity, for both the Maxwell and spin-2 case, are related to each other as they arise from the same terms in the initial data. Moreover, it is shown that this observation is true for generic data (not necessarily time-symmetric). This identification is a consequence of both the evolution and constraint equations.

中文翻译：

---

零静止质量场和平坦空间上的纽曼-彭罗斯常数

在空间无穷大附近研究了在平坦空间上传播的自旋 1（电磁场）和自旋 2 的零静止质量场及其相应的纽曼-彭罗斯 (NP) 常数。该分析的目的是阐明类空间超曲面上这些场的数据与其对应的 NP 常数在未来和过去的零无穷大值之间的对应关系。为此，使用空间无穷远圆柱体的框架来表明，将初始数据以球谐函数和测地线空间距离 $\rho$ 的幂扩展到空间无穷远，NP 常数对应于$\rho$ 中固定阶次的最高可能球谐函数。此外，对于麦克斯韦和自旋 2 的情况，未来和过去的零无穷大的 NP 常数表明，彼此相关，因为它们来自初始数据中的相同项。此外，它表明这种观察对于通用数据（不一定是时间对称的）是正确的。这种识别是演化方程和约束方程的结果。