A Coordinate-free Definition
Around 1962, Hermann Bondi, Rainer Sachs, and others began to study the general phenomenon of radiation from a compact source in general relativity, which requires more flexible definitions of asymptotic flatness. In 1963, Roger Penrose imported from algebraic geometry the essential innovation, now called conformal compactification, and in 1972, Robert Geroch used this to circumvent the tricky problem of suitably defining and evaluating suitable limits in formulating a truly coordinate-free definition of asymptotic flatness. In the new approach, once everything is properly set up, one need only evaluate functions on a locus in order to verify asymptotic flatness.
Read more about this topic: Asymptotically Flat Spacetime
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