# Derivation of the Lorentz transformation

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## Main Question or Discussion Point

I read the Lorentz transformation can be obtained by solving the requirement of invariance of the wave equation. If one considers linear transformations this the same as the spacetime interval squared to be invariant.

What are the other nonlinear transformations keeping the wave equation invariant ?
In particular shall solutions of general relativistic problems give one of those transformations ?

## Answers and Replies

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strangerep
Where?

the Lorentz transformation can be obtained by solving the requirement of invariance of the wave equation. If one considers linear transformations this the same as the spacetime interval squared to be invariant.

What are the other nonlinear transformations keeping the wave equation invariant?
If you mean electromagnetic waves, the answer is "conformal transformations",
in particular the so-called "special conformal transformations".

This recent thread is partially relevant, and contains links to more info on conformal transformations.

In particular shall solutions of general relativistic problems give one of those transformations?
I failed to any extract sensible meaning from this sentence. A "solution" of the GR field equations gives a metric, not a coordinate transformation.