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Gravitational fields near space-like and null infinity

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Friedrich,  Helmut
Geometric Analysis and Gravitation, AEI-Golm, MPI for Gravitational Physics, Max Planck Society;

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Citation

Friedrich, H. (1998). Gravitational fields near space-like and null infinity. Journal of Geometry and Physics, 24(2), 83-163. doi:10.1016/S0393-0440(97)82168-7.


Cite as: http://hdl.handle.net/11858/00-001M-0000-0013-597D-E
Abstract
Near space-like infinity an initial value problem for the conformal Einstein equations is formulated such that: (i) the data and equations are regular, (ii) space-like and null infinity have a finite representation, with their structure and location known a priori, and (iii) the setting relies entirely on general properties of conformal structures. A first analysis of this problem shows that the solutions develop in general a certain type of logarithmic singularity at the set where null infinity touches space-like infinity. These singularities form an intrinsic part of the solutions' conformal structure. Conditions on the free initial data near space-like infinity are derived which ensure that for solutions developing from these data singularities of this type cannot occur.