Newman-Penrose Constants and Their Invariant Transformations

The origin and significance of the Newman‐Penrose (N‐P) constants of the motion are examined from the point of view that constants of the motion generate invariant transformations. Here the calculation makes use of a generalization of Green's theorem to a situation applicable to the coupled Einstein‐Maxwell fields in general relativity. One finds strictly electromagnetic constants generated by an incoming electromagnetic shock wave, with dipole symmetry, at future null infinity. The gravitational constants contain an admixture from the electromagnetic field. They are generated by an incident quadrupole gravitational shock wave at future null infinity $({\mathfrak{J}}^{+})$ . Both the electromagnetic dipole field and the gravitational quadrupole field behave like linearized fields at ${\mathfrak{J}}^{+}$ . All higher‐multipole fields do not uncouple from the nonlinear corrections induced by the self‐coupling of the gravitational field and its coupling with the electromagnetic field. It is shown that the gravitational constants are related to the rate of shear of the null rays near ${\mathfrak{J}}^{+}$ a result which suggests a connection with sources. Finally, the supertranslation invariance of the result is discussed.