(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

find the transformation that turns this metric:

[tex]ds^2=-X^2dT^2+dX^2[/tex]

into the minkowski metric: diag(-1,1).

3. The attempt at a solution

attempt 1:

I transformed the above metric into the coordinates that use the lines that define the light cone as the axes. Namely,

[tex]u=T+ln(X)[/tex]

[tex]v=T-ln(X)[/tex]

attempt 2:

If I can transform the above, into the coordinates u and v such that i have

[tex] ds^2=-dudv [/tex]

then I'm done because with another transformation:

[tex]dt'=\frac{du+dv}{2}[/tex]

[tex]dx'=\frac{du-dv}{2}[/tex]

I have the relation

[tex]-(dt')^2+dx^2=-(\frac{du+dv}{2})^2+(\frac{du-dv}{2})^2=-dudv.[/tex]

Is there a systematic way of doing this?

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# Coordinate transformation to flat space

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