Abstract
It is shown that theC-metric (with parameters chosen to lie in suitable intervals) admits a conformal completion such that the space of generators of null infinity, ℐ, is a 2-sphere. This structure of ℐ is both necessary and sufficient for the analysis of gravitational radiation in exact general relativity. Bondi news (as well as the electromagnetic radiation field, in the charget case) is examined and found to be non-zero. Thus the issue of existence of exact solutions to the Einstein (and Einstein-Maxwell) equations admitting radiation (in the sense of Bondi, Sachs, and Penrose) is resolved. In addition, the analysis clarifies the sense in which the vacuumC-metric represents the gravitational field of two accelerating black-holes.
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Communicated by A. Jaffe
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Ashtekar, A., Dray, T. On the existence of solutions to Einstein's equation with non-zero Bondi news. Commun. Math. Phys. 79, 581–599 (1981). https://doi.org/10.1007/BF01209313
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DOI: https://doi.org/10.1007/BF01209313