Asymptotic Structure of Space-Time
Many physical theories have the feature that one can distinguish within the theory a certain class of models which one regards as representing “isolated systems”. In Newtonian gravitation, to take one example, one might define a solution as representing an isolated system if i) the mass density vanishes outside some compact set in the Euclidean 3-space, and ii) the Newtonian gravitational potential approaches zero in the limit far from that compact set. Normally, one would not expect that the models so distinguished will actually be realized in our World. Thus, with respect to the example above, one might expect that no matter how far one recedes from a given system in our own Universe one will encounter additional galaxies, whence i) will fail in our Universe. Nonetheless less, it turns out that the solutions so distinguished within a given theory can be of considerable physical interest, for one often encounters in the physical World systems to which these solutions are a good approximation, e.g., in the Newtonian example, our solar system. Indeed, one could perhaps argue for a much stronger statement:
KeywordsTensor Field Weyl Tensor Maxwell Field Asymptotic Structure Spatial Infinity
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- 4.R. Sachs, Proc. Roy. Soc. A270, 193 (1962).Google Scholar