Null Geodesic Congruences, Asymptotically Flat Space-Times and Their Physical Interpretation
T. M. Adamo, E. T. Newman, C. N. Kozameh
TL;DR
The paper develops a geometric framework for asymptotically flat spacetimes using shear-free and asymptotically shear-free null geodesic congruences (NGCs). Central to the approach are Good-Cut Functions (GCFs), Universal-Cut Functions (UCFs), and the auxiliary $oldsymbol{H}$-space, which together link asymptotic gravitational and Maxwell fields to complex world lines that encode the complex center of mass and, when Maxwell fields are present, the complex center of charge. Through the Newman–Penrose formalism and the Bondi framework, the authors derive evolution and flux relations for Bondi mass, linear momentum, angular momentum, and their gravitational and electromagnetic multipole contributions, including radiation reaction and recoil effects, and they show how a Dirac-like gyromagnetic ratio emerges when centers coincide. The work demonstrates a coherent, gauge-invariant picture in which interior properties are read off from asymptotic data, connecting to classical mechanics and electrodynamics, with potential links to twistor theory and holography. The results offer deep structural insights into the interplay between asymptotic infinity and interior dynamics in GR, with clear predictions and a roadmap for further exploration of holographic and twistorial structures in gravitational physics.
Abstract
Shear-free or asymptotically shear-free null geodesic congruences possess a large number of fascinating geometric properties and to be closely related, in the context of general relativity, to a variety of physically significant affects. It is the purpose of this paper to develop these issues and find applications in GR. The applications center around the problem of extracting interior physical properties of an asymptotically flat space-time directly from the asymptotic gravitational (and Maxwell) field itself in analogy with the determination of total charge by an integral over the Maxwell field at infinity or the identification of the interior mass (and its loss) by (Bondi's) integrals of the Weyl tensor, also at infinity. More specifically we will see that the asymptotically shear-free congruences lead us to an asymptotic definition of the center-of-mass and its equations of motion. This includes a kinematic meaning, in terms of the center of mass motion, for the Bondi three-momentum. In addition, we obtain insights into intrinsic spin and, in general, angular momentum, including an angular momentum conservation law with well-defined flux terms. When a Maxwell field is present the asymptotically shear-free congruences allow us to determine/define at infinity a center-of-charge world-line and intrinsic magnetic dipole moment.