Surprising structures hiding in Penrose’s future 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, In addition, almost all calculations have used the Bondi coordinate and tetrad systems. Beginning with a known asymptotically flat solution to the Einstein–Maxwell equations, we show first, that there are other natural coordinate systems, near (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 define the complex dipole moment, (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–Sachs 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, , spin, Newton’s second law with the rocket force term (v) and radiation reaction, angular momentum conservation and others. All these relations take place in the rather mysterious H-space rather than in space-time.This leads to the enigma: ‘why do these well known relations of classical mechanics take place in H-space?’ and ‘What is the physical meaning of H-space?’