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Asymptotic Structure of Space-Time: F. Esposito, L. Witten

The Symposium on Asymptotic Structure of Space-Time (SOASST) was held at the University of Cincinnati, June 14-18, 1976. We had been thinking of organizing a symposium on the properties of "infinity" for several years. The subject had reached a stage of maturity and had also formed a basis for important current investigations. Jt was felt that a symposium, together with a publication of the proceedings, would review, summarize, and consolidate, the more mature aspects of the field and serve as an appropriate introduction to an expanding body of research. We had from the first the enthusiastic support and encouragement of many colleagues; with their cooperation and advice, the Symposium acquired its final form. These proceedings will attest to the value of the Symposium. The Symposium consisted of thirty lectures and had an attendance of approximately one hundred and thirty.

The final impetus to our decision to go forward was the Bicentennial Anniversary of the independence of our country. A most appropriate celebration on a University Campus surely is an intellectual Symposium which pays honor to the histories and traditional purposes of a University. The Symposium was supported financially by the University of Cincinnati Bicentennial Committee, the National Science Foundation, the Gravity Research Foundation, and by Armand Knoblaugh, Professor Emeritus of Physics of the University of Cincinnati.

Many physical theories have the feature that one can distin- 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: It is in a sense only through a suitable notion of an isolated system that one acquires any ability at all to deal individu- individually with various subsystems in the Universe - in particular, to assign to subsystems such physical attributes as mass, angular momentum, character of emitted radiation, etc. With no ability to isolate, one would presumably be restricted to consideration only of solutions within each theory which purport to represent our verse in every detail. In effect, one would be unable to make much progress at all in physics. In any case, the standard procedure within a given theory is first to obtain a more or less precisely defined class of solutions "representing isolated systems" within the mathematical framework of the theory, and then to attribute to solutions within that class various properties of possible physical interest, relegating the approximate character of these solutions and associated properties to the point of their application to actual physical systems.

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