Hyperboloidal Cauchy data for vacuum Einstein equations and obstructions to smoothness of null infinity
- 10 May 1993
- journal article
- research article
- Published by American Physical Society (APS) in Physical Review Letters
- Vol. 70 (19) , 2829-2832
- https://doi.org/10.1103/physrevlett.70.2829
Abstract
Various works have suggested that the Bondi-Sachs-Penrose decay conditions on the gravitational field at null infinity are not generally representative of asymptotically flat spacetimes. We have made a detailed analysis of the constraint equations for ‘‘asymptotically hyperboloidal’’ initial data and find that log terms arise generically in asymptotic expansions. These terms are absent in the corresponding Bondi-Sachs-Penrose expansions, and can be related to explicit geometric quantities. We have nevertheless shown that there exists a large class of ‘‘nongeneric’’ solutions of the constraint equations, the evolution of which leads to spacetimess satisfying the Bondi-Sachs-Penrose smoothness conditions.Keywords
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