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Homogeneous Projective Coordinates for the Bondi-Metzner-Sachs Group
Version 1
: Received: 2 June 2024 / Approved: 3 June 2024 / Online: 4 June 2024 (08:47:51 CEST)
A peer-reviewed article of this Preprint also exists.
Esposito, G.; Vitale, G.F. Homogeneous Projective Coordinates for the Bondi–Metzner–Sachs Group. Symmetry 2024, 16, 867. Esposito, G.; Vitale, G.F. Homogeneous Projective Coordinates for the Bondi–Metzner–Sachs Group. Symmetry 2024, 16, 867.
Abstract
This paper studies the Bondi-Metzner-Sachs group in homogeneous
projective coordinates, because it is then possible to write all
transformations of such a group in a manifestly linear way.
The 2-sphere metric, Bondi-Metzner-Sachs metric, asymptotic Killing
vectors, generators of supertranslations,
as well as boosts and rotations of Minkowski spacetime, are
all re-expressed in homogeneous projective coordinates.
Last, the integral curves of vector fields which generate supertranslations
are evaluated in detail. This work prepares the ground for more advanced
applications of the differential geometry of asymptotically flat
spacetimes in projective coordinates.
Keywords
Vector fields; Bondi-Metzner-Sachs group; homogeneous projective coordinates
Subject
Physical Sciences, Mathematical Physics
Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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