# Surprising Structures Hiding at Penrose's Future Null Infinity

## TL;DR

The paper introduces new coordinate systems near Penrose's null infinity that reveal hidden structures, allowing definitions of physical quantities like dipole moments and deriving classical mechanics results from asymptotic spacetime properties.

## Contribution

It presents novel shear-free null congruence coordinates at null infinity and connects asymptotic gravitational data to classical mechanics and electrodynamics results.

## Key findings

- Defined complex dipole moments from asymptotic Weyl tensor components.
- Derived classical mechanics relations from asymptotic spacetime structures.
- Identified new coordinate systems revealing hidden structures at null infinity.

## Abstract

Since the late1950s, almost all discussions of Asymptotically Flat (Einstein-Maxwell) Space-Times have taken place in the context of Penrose's Null Infinity, $\mathcal{I}^{+}.$\ $\ $In addition,\ almost all calculations have used the Bondi coordinate and tetrad systems. \ We show - first, that there are other natural coordinate systems, near $\mathcal{I}^{+},$ (analogous to light-cones in flat-space) that are based on (asymptotically) shear-free null geodesic congruences (analogous to the flat-space case). \ Using these new coordinates and their associated tetrad, we \textit{define the complex dipole moment, i.e., as the mass dipole plus i times angular momentum,} from the $l=1,\ $harmonic coefficient of a component of the asymptotic$\ $Weyl tensor. Second, from this definition, from the Bianchi Identities and from the Bondi mass and linear momentum, we show that \ there exists a large number of results - identifications and dynamics - identical to those of classical mechanics and electrodynamics. They include, among many others, \textbf{P}=M\textbf{v}+..., \textbf{L}=\textbf{r}x\textbf{P}, \ spin, Newtons 2nd Law with the Rocket force term (\.{M}\textbf{v}) and radiation reaction, angular momentum conservation and others. \ All these relations take place in the rather mysterious H-Space.