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Surprising Structures Hiding at Penrose's Future Null Infinity

Published 29 Jan 2017 in gr-qc | (1701.08406v1)

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, I<sup>+.\mathcal{I}<sup>{+}.\  \ In addition,\ almost all calculations have used the Bondi coordinate and tetrad systems. \ We show - first, that there are other natural coordinate systems, near I<sup>+,\mathcal{I}<sup>{+}, (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, 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.

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