# Conformal transformation

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It is often profitable to study nonlinear wave equations using **conformal transformations of spacetime**. The Lorentz transformations, translations, scaling, and time reversal are the most obvious examples, but conformal compactification (mapping conformally to a compact subset of known as the Einstein diamond) is also very useful, especially for global well-posedness and scattering theory. One can also blow up spacetime around a singularity in order to analyze the behaviour near that singularity better.