A changed perspective concerning asymptotically flat Einstein/Einstein–Maxwell space–times
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Approximately 60 years ago, Herman Bondi took the major step in the study of gravitational radiation of introducing the use of null surfaces as coordinates for the study and integration of the Einstein equations. This led to the well-known Bondi mass loss theorem, the basis of the recent observation by the Ligo team of gravitational radiation. In Bondi’s approach to the integration procedure, he used special null surfaces (now referred to as Bondi null surfaces) where the null generators possessed (in general) non-vanishing asymptotic shear—the free radiation data. The use of this Bondi strategy over the years has become almost sacrosanct—being the central approach in almost all discussions of gravitational radiation issues. It led to the idea of an asymptotic symmetry—the BMS group. Eventually Bondi’s description of null infinity became elegantly formalized via Penrose’s future null infinity and associated structures. However recently an alternative picture of null infinity has been developed—now based on the similarity of the null surfaces to those of flat-space near null infinity. The new null surfaces, that are now asymptotically shear-free, are very different from the Bondi surfaces. These surfaces are as similar as possible to flat-space light cones near infinity. Totally new structures—e.g., the geometric asymptotically shear-free null geodesic congruences and even the physical classical equations of motion, now appear in this new picture. The Bondi–Sachs energy–momentum conservations laws remain but are augmented by angular momentum (orbital and spin) conservation laws. The BMS group again reappears, not as an asymptotic symmetry group, but as a transformation group acting on these new structures. An unanswered question arises: with this new point of view, have we lost the asymptotic symmetries of the BMS group?
KeywordsAsymptotically flat Einstein–Maxwell Shear-free
We thank Timothy Adamo for many hours of enlightening and fruitful discussions and collaboration on earlier manuscripts where many of the ideas were developed. Roger Penrose is owed, almost beyond thanks, for his insights, encouragement and suggestions.